Remarks on the Asymptotic Hecke Algebra
Let G be a split reductive p-adic group, I ⊂ G be an Iwahori subgroup, H(G) be the Hecke algebra and C(G) ⊃ H(G) be the Harish-Chandra Schwartz algebra. The purpose of this note is to define (in spectral terms) a subalgebra J(G) of C(G), containing H(G), which we consider as an algebraic version of C(G). We show that the subalgebra J(G)I×I ⊂ J(G) is isomorphic to the Lusztig’s asymptotic Hecke algebra J and explain a relation between the algebra J(G) and the Schwartz space of the basic affine space studied in .
KeywordsHecke algebras p-adic groups
Mathematics Subject Classification (2010):20C11 22D10 22D20
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