Semisimple types for p-adic classical groups

Michitaka Miyauchi; Shaun Stevens

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arXiv · 1212.0525

Semisimple types for p-adic classical groups

Michitaka Miyauchi·Shaun Stevens

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Abstract

We construct, for any symplectic, unitary or special orthogonal group over a locally compact nonarchimedean local field of odd residual characteristic, a type for each Bernstein component of the category of smooth representations, using Bushnell--Kutzko's theory of covers. Moreover, for a component corresponding to a cuspidal representation of a maximal Levi subgroup, we prove that the Hecke algebra is either abelian, or a generic Hecke algebra on an infinite dihedral group, with parameters which are, at least in principle, computable via results of Lusztig.

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BibTeX RIS

Michitaka Miyauchi, Shaun Stevens. 2012-12-03. Semisimple types for p-adic classical groups. https://arxiv.org/abs/1212.0525

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