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

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 GL(n)(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.