@inbook{42e4d8510580406ca7f46bc190419946,

title = "Remarks on the asymptotic hecke algebra",

abstract = "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{\textquoteright}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 [2].",

keywords = "Hecke algebras, p-adic groups",

author = "Alexander Braverman and David Kazhdan",

year = "2018",

doi = "10.1007/978-3-030-02191-7_4",

language = "English",

series = "Progress in Mathematics",

publisher = "Springer Basel",

pages = "91--108",

booktitle = "Progress in Mathematics",

}