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- Title
On endomorphism algebras of Gelfand-Graev representations.
- Authors
Li, Tzu-Jan
- Abstract
For a connected reductive group G defined over \mathbb {F}_q and equipped with the induced Frobenius endomorphism F, we study the relation among the following three \mathbb {Z}-algebras: (i) the \mathbb {Z}-model \mathsf {E}_G of endomorphism algebras of Gelfand-Graev representations of G^F; (ii) the Grothendieck group \mathsf {K}_{G^\ast } of the category of representations of G^{\ast F^\ast } over \overline {\mathbb {F}_q} (Deligne-Lusztig dual side); (iii) the ring \mathsf {B}_{G^\vee } of the scheme (T^\vee /\!\!/ W)^{F^\vee } over \mathbb {Z} (Langlands dual side). The comparison between (i) and (iii) is motivated by recent advances in the local Langlands program.
- Subjects
REPRESENTATIONS of algebras; ENDOMORPHISMS; GROTHENDIECK groups
- Publication
Representation Theory, 2023, Vol 27, p80
- ISSN
1088-4165
- Publication type
Article
- DOI
10.1090/ert/627