{"id":"https://openalex.org/W7202188736","doi":"https://doi.org/10.48550/arxiv.2608.08813","title":"Stable $q$-Hermitian coordinate calculus: Capelli--PBW transport, mixed polarization algebra, and localization obstructions","display_name":"Stable $q$-Hermitian coordinate calculus: Capelli--PBW transport, mixed polarization algebra, and localization obstructions","publication_year":2026,"publication_date":"2026-08-09","ids":{"openalex":"https://openalex.org/W7202188736","doi":"https://doi.org/10.48550/arxiv.2608.08813"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.08813","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.08813","pdf_url":"https://arxiv.org/pdf/2608.08813","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.08813","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5076794735","display_name":"Baruch Schneider","orcid":"https://orcid.org/0000-0002-5122-3576","observed_orcids":["https://orcid.org/0000-0002-5122-3576","https://orcid.org/0000-0003-2933-3899"]},"institutions":[{"id":"https://openalex.org/I187293425","display_name":"University of Ostrava","ror":"https://ror.org/00pyqav47","country_code":"CZ","type":"education","lineage":["https://openalex.org/I187293425"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Schneider, Baruch","raw_affiliation_strings":["Department of Mathematics , University of Ostrava , 70200 Ostrava , Czechia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , University of Ostrava , 70200 Ostrava , Czechia","institution_ids":["https://openalex.org/I187293425"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5092715746","display_name":"Diana Schneiderov\u00e1","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Schneiderov\u00e1, Diana","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5159809231","display_name":"Yifan Zhang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I187293425","display_name":"University of Ostrava","ror":"https://ror.org/00pyqav47","country_code":"CZ","type":"education","lineage":["https://openalex.org/I187293425"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Zhang, Yifan","raw_affiliation_strings":["Department of Mathematics , University of Ostrava , 70200 Ostrava , Czechia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , University of Ostrava , 70200 Ostrava , Czechia","institution_ids":["https://openalex.org/I187293425"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12037","display_name":"Algebraic and Geometric Analysis","score":0.8525000214576721,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12037","display_name":"Algebraic and Geometric Analysis","score":0.8525000214576721,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.050599999725818634,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.03629999980330467,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/clifford-algebra","display_name":"Clifford algebra","score":0.6629999876022339},{"id":"https://openalex.org/keywords/capelli-identities","display_name":"Capelli identities","score":0.48100000619888306},{"id":"https://openalex.org/keywords/pbw-theorem","display_name":"PBW theorem","score":0.7730000019073486},{"id":"https://openalex.org/keywords/q-deformation","display_name":"q-deformation","score":0.5080000162124634}],"concepts":[{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.7060999870300293},{"id":"https://openalex.org/C169611556","wikidata":"https://www.wikidata.org/wiki/Q230689","display_name":"Contractible space","level":2,"score":0.6759999990463257},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6690000295639038},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.4921000003814697},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.46050000190734863},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.450300008058548},{"id":"https://openalex.org/C80551277","wikidata":"https://www.wikidata.org/wiki/Q11210","display_name":"Coordinate system","level":2,"score":0.43529999256134033},{"id":"https://openalex.org/C205049153","wikidata":"https://www.wikidata.org/wiki/Q2698605","display_name":"Polarization (electrochemistry)","level":2,"score":0.4350999891757965},{"id":"https://openalex.org/C100856211","wikidata":"https://www.wikidata.org/wiki/Q674689","display_name":"Clifford algebra","level":3,"score":0.43299999833106995},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.42329999804496765},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.40549999475479126},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3889999985694885},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.35260000824928284},{"id":"https://openalex.org/C98214594","wikidata":"https://www.wikidata.org/wiki/Q850275","display_name":"Conformal map","level":2,"score":0.3521000146865845},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3228999972343445},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.32010000944137573},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3160000145435333},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.3070000112056732},{"id":"https://openalex.org/C110521144","wikidata":"https://www.wikidata.org/wiki/Q193460","display_name":"Scalar field","level":2,"score":0.305400013923645},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.29840001463890076},{"id":"https://openalex.org/C94863793","wikidata":"https://www.wikidata.org/wiki/Q1196652","display_name":"Exterior algebra","level":3,"score":0.2955999970436096},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.29269999265670776},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.28279998898506165},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.27810001373291016},{"id":"https://openalex.org/C84316537","wikidata":"https://www.wikidata.org/wiki/Q36255","display_name":"Unit vector","level":2,"score":0.2680000066757202},{"id":"https://openalex.org/C83979697","wikidata":"https://www.wikidata.org/wiki/Q1778247","display_name":"Codimension","level":2,"score":0.2535000145435333},{"id":"https://openalex.org/C181830111","wikidata":"https://www.wikidata.org/wiki/Q214850","display_name":"Gauge theory","level":2,"score":0.25200000405311584},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.2502000033855438}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.08813","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.08813","pdf_url":"https://arxiv.org/pdf/2608.08813","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.08813","doi":"https://doi.org/10.48550/arxiv.2608.08813","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.08813","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.08813","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.08813","pdf_url":"https://arxiv.org/pdf/2608.08813","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1329213119","display_name":null,"funder_award_id":"SGS05","funder_id":"https://openalex.org/F4320324050","funder_display_name":"Ostravsk\u00e1 Univerzita v Ostrav\u011b"},{"id":"https://openalex.org/G1635208302","display_name":"Combinatorial structures, continuous mathematics and their impact on the design of efficient algorithms","funder_award_id":"GA25-16847S","funder_id":"https://openalex.org/F4320321006","funder_display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky"}],"funders":[{"id":"https://openalex.org/F4320321006","display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky","ror":"https://ror.org/01pv73b02"},{"id":"https://openalex.org/F4320324050","display_name":"Ostravsk\u00e1 Univerzita v Ostrav\u011b","ror":"https://ror.org/00pyqav47"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7202188736.pdf","grobid_xml":"https://content.openalex.org/works/W7202188736.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2262396538","https://openalex.org/W7116121073","https://openalex.org/W7171396754","https://openalex.org/W7100629224","https://openalex.org/W4384389979","https://openalex.org/W2072404880","https://openalex.org/W1137667336","https://openalex.org/W7098499701","https://openalex.org/W7099881849","https://openalex.org/W3103477667"],"abstract_inverted_index":{"We":[0],"extend":[1],"a":[2,27,43,109,129],"finite-support":[3],"$q$-Hermitian":[4,71],"radial":[5,85],"calculus":[6],"to":[7,52,62,83,166],"Clifford-valued":[8],"coordinate":[9,72,125],"polynomials.":[10],"For":[11,103],"$N$":[12],"bosonic":[13],"Hermitian":[14,97],"vector":[15],"labels":[16],"and":[17,93,127,145,156],"finite":[18,44,138,153,157],"fermionic":[19,64,158],"support,":[20],"the":[21,39,48,53,59,84,95,104,117,123,146,170],"stable":[22],"range":[23],"$m\\ge":[24],"2N$":[25],"admits":[26],"canonical":[28],"Gram--harmonic":[29],"normal":[30],"form":[31],"by":[32],"Howe":[33],"separation.":[34],"A":[35],"label--Capelli":[36],"inverse":[37],"normalizes":[38],"Clifford":[40,55],"contractions,":[41],"while":[42],"Wick--Chevalley":[45],"conjugation":[46],"lifts":[47],"divided-power":[49],"scalar":[50,89],"gauge":[51],"full":[54,124,172],"PBW":[56,86],"module.":[57],"Coupling":[58],"normalized":[60,118],"contractions":[61,120],"contractible":[63],"seed":[65],"complexes":[66],"gives":[67],"two":[68,171],"conjugate":[69],"polynomial-preserving":[70],"families.":[73],"They":[74],"are":[75,137,176],"square-zero,":[76],"anticommute":[77],"within":[78],"each":[79],"polarization,":[80],"restrict":[81],"exactly":[82],"calculus,":[87],"have":[88],"boundary":[90],"trace":[91],"$[2m-2n]_q$,":[92],"recover":[94],"classical":[96,161],"super":[98],"Dirac":[99],"pair":[100],"as":[101],"$q\\to1$.":[102],"mixed":[105,135,147],"polarizations":[106],"we":[107],"introduce":[108],"relative":[110],"triangular":[111],"transport.":[112],"The":[113,160],"Grassmann":[114],"relations":[115],"for":[116,151,178],"Capelli":[119],"hold":[121],"on":[122],"module":[126],"yield":[128],"labelwise":[130],"factorization.":[131],"Hence":[132],"all":[133],"higher-filtration":[134],"terms":[136],"subset":[139],"products":[140,175],"of":[141],"explicit":[142],"local":[143],"defects,":[144],"polarization":[148],"algebra":[149],"closes":[150],"arbitrary":[152],"label":[154],"sets":[155],"support.":[159],"complex":[162],"structure":[163],"is":[164],"common":[165],"both":[167],"polarizations,":[168],"whereas":[169],"transported":[173],"Clifford--Weyl":[174],"distinct":[177],"$0":[179]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-08-12T00:00:00"}