Formal degree of regular supercuspidals

Formal degree of regular supercuspidals

Supercuspidal representations are usually infinite-dimensional, so the size of such a representation cannot be measured by its dimension; the formal degree is a better alternative. Hiraga, Ichino, and Ikeda conjectured a formula for the formal degree of a supercuspidal in terms of its L -parameter o...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Journal of the European Mathematical Society : JEMS 2024-01, Vol.26 (10), p.3685-3737
1. Verfasser: Schwein, David
Format: Artikel
Sprache:eng
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page 3737
container_issue 10
container_start_page 3685
container_title Journal of the European Mathematical Society : JEMS
container_volume 26
creator Schwein, David
description Supercuspidal representations are usually infinite-dimensional, so the size of such a representation cannot be measured by its dimension; the formal degree is a better alternative. Hiraga, Ichino, and Ikeda conjectured a formula for the formal degree of a supercuspidal in terms of its L -parameter only. Our first main result is to compute the formal degrees of the supercuspidal representations constructed by Yu. Our second result, using the first, is to verify that Kaletha’s regular supercuspidal L -packets satisfy the conjecture.
doi_str_mv 10.4171/jems/1412
format Article
fullrecord <record><control><sourceid>crossref</sourceid><recordid>TN_cdi_crossref_primary_10_4171_jems_1412</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>10_4171_jems_1412</sourcerecordid><originalsourceid>FETCH-LOGICAL-c119t-6f22f3b9e797daa7e16bc319667cf9c8d6ea25f6e7c7dd0a54aac6495a623c963</originalsourceid><addsrcrecordid>eNo9z01LAzEUheEgCtbqwn8wO3ExNjcfN81SilWh4EbX4Ta5KS0zzJA4C_-9Doqr96wOPELcgnww4GB14r6uwIA6Ewsw2rZ-jfr8f1t7Ka5qPUkJzhq9EHfbofTUNYkPhbkZclP4MHVUmjqNXOJUx2Oirl6Li_wTvvnrUnxsn943L-3u7fl187hrI4D_bDErlfXes_MuETkG3EcNHtHF7OM6IZOyGdlFl5Ika4giGm8JlY4e9VLc__7GMtRaOIexHHsqXwFkmIVhFoZZqL8B8cVESQ</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Formal degree of regular supercuspidals</title><source>DOAJ Directory of Open Access Journals</source><source>EZB-FREE-00999 freely available EZB journals</source><creator>Schwein, David</creator><creatorcontrib>Schwein, David</creatorcontrib><description>Supercuspidal representations are usually infinite-dimensional, so the size of such a representation cannot be measured by its dimension; the formal degree is a better alternative. Hiraga, Ichino, and Ikeda conjectured a formula for the formal degree of a supercuspidal in terms of its L -parameter only. Our first main result is to compute the formal degrees of the supercuspidal representations constructed by Yu. Our second result, using the first, is to verify that Kaletha’s regular supercuspidal L -packets satisfy the conjecture.</description><identifier>ISSN: 1435-9855</identifier><identifier>EISSN: 1435-9863</identifier><identifier>DOI: 10.4171/jems/1412</identifier><language>eng</language><ispartof>Journal of the European Mathematical Society : JEMS, 2024-01, Vol.26 (10), p.3685-3737</ispartof><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><orcidid>0000-0001-9679-3030</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,864,27924,27925</link.rule.ids></links><search><creatorcontrib>Schwein, David</creatorcontrib><title>Formal degree of regular supercuspidals</title><title>Journal of the European Mathematical Society : JEMS</title><description>Supercuspidal representations are usually infinite-dimensional, so the size of such a representation cannot be measured by its dimension; the formal degree is a better alternative. Hiraga, Ichino, and Ikeda conjectured a formula for the formal degree of a supercuspidal in terms of its L -parameter only. Our first main result is to compute the formal degrees of the supercuspidal representations constructed by Yu. Our second result, using the first, is to verify that Kaletha’s regular supercuspidal L -packets satisfy the conjecture.</description><issn>1435-9855</issn><issn>1435-9863</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNo9z01LAzEUheEgCtbqwn8wO3ExNjcfN81SilWh4EbX4Ta5KS0zzJA4C_-9Doqr96wOPELcgnww4GB14r6uwIA6Ewsw2rZ-jfr8f1t7Ka5qPUkJzhq9EHfbofTUNYkPhbkZclP4MHVUmjqNXOJUx2Oirl6Li_wTvvnrUnxsn943L-3u7fl187hrI4D_bDErlfXes_MuETkG3EcNHtHF7OM6IZOyGdlFl5Ika4giGm8JlY4e9VLc__7GMtRaOIexHHsqXwFkmIVhFoZZqL8B8cVESQ</recordid><startdate>20240122</startdate><enddate>20240122</enddate><creator>Schwein, David</creator><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0001-9679-3030</orcidid></search><sort><creationdate>20240122</creationdate><title>Formal degree of regular supercuspidals</title><author>Schwein, David</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c119t-6f22f3b9e797daa7e16bc319667cf9c8d6ea25f6e7c7dd0a54aac6495a623c963</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Schwein, David</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of the European Mathematical Society : JEMS</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Schwein, David</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Formal degree of regular supercuspidals</atitle><jtitle>Journal of the European Mathematical Society : JEMS</jtitle><date>2024-01-22</date><risdate>2024</risdate><volume>26</volume><issue>10</issue><spage>3685</spage><epage>3737</epage><pages>3685-3737</pages><issn>1435-9855</issn><eissn>1435-9863</eissn><abstract>Supercuspidal representations are usually infinite-dimensional, so the size of such a representation cannot be measured by its dimension; the formal degree is a better alternative. Hiraga, Ichino, and Ikeda conjectured a formula for the formal degree of a supercuspidal in terms of its L -parameter only. Our first main result is to compute the formal degrees of the supercuspidal representations constructed by Yu. Our second result, using the first, is to verify that Kaletha’s regular supercuspidal L -packets satisfy the conjecture.</abstract><doi>10.4171/jems/1412</doi><tpages>53</tpages><orcidid>https://orcid.org/0000-0001-9679-3030</orcidid><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 1435-9855
ispartof Journal of the European Mathematical Society : JEMS, 2024-01, Vol.26 (10), p.3685-3737
issn 1435-9855
1435-9863
language eng
recordid cdi_crossref_primary_10_4171_jems_1412
source DOAJ Directory of Open Access Journals; EZB-FREE-00999 freely available EZB journals
title Formal degree of regular supercuspidals
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-26T09%3A40%3A22IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-crossref&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Formal%20degree%20of%20regular%20supercuspidals&rft.jtitle=Journal%20of%20the%20European%20Mathematical%20Society%20:%20JEMS&rft.au=Schwein,%20David&rft.date=2024-01-22&rft.volume=26&rft.issue=10&rft.spage=3685&rft.epage=3737&rft.pages=3685-3737&rft.issn=1435-9855&rft.eissn=1435-9863&rft_id=info:doi/10.4171/jems/1412&rft_dat=%3Ccrossref%3E10_4171_jems_1412%3C/crossref%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true