HECKE ALGEBRAS FOR INNER FORMS OF p-ADIC SPECIAL LINEAR GROUPS

Anne Marie Aubert, Paul Baum, Roger Plymen, Maarten Solleveld

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Abstract

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 languageEnglish (US)
Pages (from-to)351-419
Number of pages69
JournalJournal of the Institute of Mathematics of Jussieu
Volume16
Issue number2
DOIs
StatePublished - Apr 1 2017

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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