ON ENDOMORPHISM ALGEBRAS OF GELFAND-GRAEV REPRESENTATIONS

For a connected reductive group G defined over Fq and equipped with the induced Frobenius endomorphism F, we study the relation among the following three Z -algebras: (i) the Z -model EG of endomorphism algebras of Gelfand-Graev representations of GF; (ii) the Grothendieck group KG* of the category of representations of G*F* over Fq (Deligne-Lusztig dual side); (iii) the ring BGv of the scheme (Tv//W)Fv over Z (Langlands dual side). The comparison between (i) and (iii) is motivated by recent advances in the local Langlands program.