On endomorphism algebras of Gelfand-Graev representations
Résumé
For a connected reductive group G defined over F q and equipped with the induced Frobenius endomorphism F , we study the relation among the following three Z-algebras: (i) the Z-model E G of endomorphism algebras of Gelfand-Graev representations of G F ; (ii) the Grothendieck group K G * of the category of representations of G * F * over F q (Deligne-Lusztig dual side); (iii) the ring B G ∨ of the scheme (T ∨ W) F ∨ over Z (Langlands dual side). The comparison between (i) and (iii) is motivated by recent advances in the local Langlands program.
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