Smooth representations of GLm(D) VI: Semisimple types

Vincent Sécherre, Shaun Stevens

Research output: Contribution to journalArticlepeer-review

31 Citations (Scopus)


We give a complete description of the category of smooth complex representations of the multiplicative group of a central simple algebra over a locally compact nonarchimedean local field. More precisely, for each inertial class in the Bernstein spectrum, we construct a type and compute its Hecke algebra. The Hecke algebras that arise are all naturally isomorphic to products of affine Hecke algebras of type A. We also prove that, for cuspidal classes, the simple type is unique up to conjugacy.
Original languageEnglish
Pages (from-to)2994-3039
Number of pages46
JournalInternational Mathematics Research Notices
Issue number13
Early online date6 Jul 2011
Publication statusPublished - 2012

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