The Bernstein presentation for general connected reductive groups
arXiv:1312.7374 · doi:10.1112/jlms/jdu080
Abstract
Let F be a non-Archimedean local field and let G be a connected reductive affine algebraic F-group. Let I be an Iwahori subgroup of G(F) and denote by H(G; I) the Iwahori-Hecke algebra, i.e. the convolution algebra of complex-valued functions on G(F) which are left- and right-invariant by I-translations. This article proves that the Iwahori-Hecke algebra H(G; I) has both an Iwahori-Matsumoto Presentation and a Bernstein Presentation analogous to those for affine Hecke algebras on root data found in Lusztig's "Affine Hecke algebras and their graded version", and gives a basis (in other words, an explicit Bernstein Isomorphism) for the center Z[H(G; I)] also analogous to that found in loc. cit.
24 pages, referee response incorporated (to appear in J. London Math. Soc.), acknowledgements added, diagrams finally upgraded from "matrix" style to amscd, several other minor corrections and edits; should be final version