TY - JOUR

T1 - HECKE ALGEBRAS FOR INNER FORMS OF p-ADIC SPECIAL LINEAR GROUPS

AU - Aubert, Anne Marie

AU - Baum, Paul

AU - Plymen, Roger

AU - Solleveld, Maarten

N1 - Funding Information:
The second author was partially supported by NSF grant DMS-1200475.
Publisher Copyright:
© 2015 Cambridge University Press.

PY - 2017/4/1

Y1 - 2017/4/1

N2 - 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.

AB - 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.

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U2 - 10.1017/S1474748015000079

DO - 10.1017/S1474748015000079

M3 - Article

AN - SCOPUS:84928818068

VL - 16

SP - 351

EP - 419

JO - Journal of the Institute of Mathematics of Jussieu

JF - Journal of the Institute of Mathematics of Jussieu

SN - 1474-7480

IS - 2

ER -