A triangular system for local character expansions of Iwahori-spherical representations of general linear groups
For Iwahori-spherical representations of non-Archimedean general linear groups, Chan–Savin recently expressed the Whittaker functor as a restriction to an isotypic component of a finite Iwahori–Hecke algebra module. We generalize this method to describe principal degenerate Whittaker functors. Concu...
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Académie des sciences
2023-01-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.384/ |
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| author | Gurevich, Maxim |
| author_facet | Gurevich, Maxim |
| author_sort | Gurevich, Maxim |
| collection | DOAJ |
| description | For Iwahori-spherical representations of non-Archimedean general linear groups, Chan–Savin recently expressed the Whittaker functor as a restriction to an isotypic component of a finite Iwahori–Hecke algebra module. We generalize this method to describe principal degenerate Whittaker functors. Concurrently, we view Murnaghan’s formula for the Harish-Chandra–Howe character as a Grothendieck group expansion of the same module.Comparing the two approaches through the lens of Zelevinsky’s PSH-algebras, we obtain an explicit unitriangular transition matrix between coefficients of the character expansion and the principal degenerate Whittaker dimensions. |
| format | Article |
| id | doaj-art-f2c39ca7d61e46498b21e7f262d05bb8 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-f2c39ca7d61e46498b21e7f262d05bb82025-02-07T11:06:07ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-01-01361G1213010.5802/crmath.38410.5802/crmath.384A triangular system for local character expansions of Iwahori-spherical representations of general linear groupsGurevich, Maxim0Department of Mathematics, Technion – Israel Institute of Technology, Haifa, IsraelFor Iwahori-spherical representations of non-Archimedean general linear groups, Chan–Savin recently expressed the Whittaker functor as a restriction to an isotypic component of a finite Iwahori–Hecke algebra module. We generalize this method to describe principal degenerate Whittaker functors. Concurrently, we view Murnaghan’s formula for the Harish-Chandra–Howe character as a Grothendieck group expansion of the same module.Comparing the two approaches through the lens of Zelevinsky’s PSH-algebras, we obtain an explicit unitriangular transition matrix between coefficients of the character expansion and the principal degenerate Whittaker dimensions.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.384/ |
| spellingShingle | Gurevich, Maxim A triangular system for local character expansions of Iwahori-spherical representations of general linear groups Comptes Rendus. Mathématique |
| title | A triangular system for local character expansions of Iwahori-spherical representations of general linear groups |
| title_full | A triangular system for local character expansions of Iwahori-spherical representations of general linear groups |
| title_fullStr | A triangular system for local character expansions of Iwahori-spherical representations of general linear groups |
| title_full_unstemmed | A triangular system for local character expansions of Iwahori-spherical representations of general linear groups |
| title_short | A triangular system for local character expansions of Iwahori-spherical representations of general linear groups |
| title_sort | triangular system for local character expansions of iwahori spherical representations of general linear groups |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.384/ |
| work_keys_str_mv | AT gurevichmaxim atriangularsystemforlocalcharacterexpansionsofiwahorisphericalrepresentationsofgenerallineargroups AT gurevichmaxim triangularsystemforlocalcharacterexpansionsofiwahorisphericalrepresentationsofgenerallineargroups |