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Generic and mod p Kazhdan-Lusztig Theory for GL_2.
- Source :
-
Representation Theory . 11/29/2023, Vol. 27, p1142-1193. 52p. - Publication Year :
- 2023
-
Abstract
- Let F be a non-archimedean local field with residue field \mathbb {F}_q and let \mathbf {G}=GL_{2/F}. Let \mathbf {q} be an indeterminate and let \mathcal {H}^{(1)}(\mathbf {q}) be the generic pro-p Iwahori-Hecke algebra of the p-adic group \mathbf {G}(F). Let V_{\mathbf {\widehat {G}}} be the Vinberg monoid of the dual group \mathbf {\widehat {G}}. We establish a generic version for \mathcal {H}^{(1)}(\mathbf {q}) of the Kazhdan-Lusztig-Ginzburg spherical representation, the Bernstein map and the Satake isomorphism. We define the flag variety for the monoid V_{\mathbf {\widehat {G}}} and establish the characteristic map in its equivariant K-theory. These generic constructions recover the classical ones after the specialization \mathbf {q}=q\in \mathbb {C}. At \mathbf {q}=q=0\in \overline {\mathbb {F}}_q, the spherical map provides a dual parametrization of all the irreducible \mathcal {H}^{(1)}_{\overline {\mathbb {F}}_q}(0)-modules. [ABSTRACT FROM AUTHOR]
- Subjects :
- *K-theory
*GROUP algebras
*ISOMORPHISM (Mathematics)
Subjects
Details
- Language :
- English
- ISSN :
- 10884165
- Volume :
- 27
- Database :
- Academic Search Index
- Journal :
- Representation Theory
- Publication Type :
- Academic Journal
- Accession number :
- 173919852
- Full Text :
- https://doi.org/10.1090/ert/656