Let F be a non-Archimedean local field, and let G# be the group of F-rational points of an inner form of SLn. We study Hecke algebras for all Bernstein components of G#, via restriction from an inner form G of GLn(F). For any packet of L-indistinguishable Bernstein components, we exhibit an explicit algebra whose module category is equivalent to the associated category of complex smooth G#-representations. This algebra comes from an idempotent in the full Hecke algebra of G#, and the idempotent is derived from a type for G. We show that the Hecke algebras for Bernstein components of G# are similar to affine Hecke algebras of type A, yet in many cases are not Morita equivalent to any crossed product of an affine Hecke algebra with a finite group.
|Original language||English (US)|
|Number of pages||69|
|Journal||Journal of the Institute of Mathematics of Jussieu|
|State||Published - Apr 1 2017|
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