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 SL_n. 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.