# Cuspidal irreducible representations of quaternionic forms of p-adic classical groups for odd p

@article{Skodlerack2019CuspidalIR, title={Cuspidal irreducible representations of quaternionic forms of p-adic classical groups for odd p}, author={Daniel Skodlerack}, journal={arXiv: Representation Theory}, year={2019} }

Given a quaternionic form G of a p-adic classical group ($p$ odd) we classify all cuspidal irreducible complex representations of G. It is a straight forward generalization of the classification in the p-adic classical group case. We prove two theorems: At first: Every irreducible cuspidal representation of G is induced from a cuspidal type, i.e. from a certain irreducible representation of a compact open subgroup of G, constructed from a beta-extension and a cuspidal representation of a finite… Expand

#### 2 Citations

Comparison of Bushnell-Kutzko and Yu's constructions of supercuspidal representations

- Mathematics
- 2020

We compare precisely and explicitly Bushnell-Kutzko and Yu's constructions of supercuspidal representations. At the end, we draw conclusions and ask a natural question about the existence of a… Expand

Representations of a reductive $p$-adic group in characteristic distinct from $p$

- Mathematics
- 2020

We investigate the irreducible cuspidal $C$-representations of a reductive $p$-adic group $G$ over a field $C$ of characteristic different from $p$. When $C$ is algebraically closed, for many groups… Expand

#### References

SHOWING 1-10 OF 38 REFERENCES

Cuspidal ℓ-modular representations of p-adic classical groups

- Mathematics
- 2015

Abstract For a classical group over a non-archimedean local field of odd residual characteristic p, we construct all cuspidal representations over an arbitrary algebraically closed field of… Expand

Semisimple types for $$p$$p-adic classical groups

- Mathematics
- 2012

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… Expand

Tame cuspidal representations in non-defining characteristics

- Mathematics
- 2019

Let k be a non-archimedean local field of odd residual characteristic p. Let G be a (connected) reductive group that splits over a tamely ramified field extension of k. We revisit Yu's construction… Expand

Endo-parameters for p-adic classical groups

- Mathematics
- 2016

For a classical group over a non-archimedean local field of odd residual characteristic p, we prove that two cuspidal types, defined over an algebraically closed field C of characteristic different… Expand

Semisimple characters for p-adic classical groups

- Mathematics
- 2005

Let G be a unitary, symplectic, or orthogonal group over a non-Archimedean local field of residual characteristic different from 2, considered as the fixed-point subgroup in a general linear group of… Expand

Endo-classes for p-adic classical groups

- Mathematics
- 2016

For a unitary, symplectic, or special orthogonal group over a non-archimedean local field of odd residual characteristic, we prove that two intertwining cuspidal types are conjugate in the group.… Expand

Semisimple Types in GLn

- Mathematics
- 1999

This paper is concerned with the smooth representation theory of the general linear group G=GL(F) of a non-Archimedean local field F. The point is the (explicit) construction of a special series of… Expand

The supercuspidal representations of p-adic classical groups

- Mathematics
- 2006

Let G be a unitary, symplectic or special orthogonal group over a locally compact non-archimedean local field of odd residual characteristic. We construct many new supercuspidal representations of G,… Expand

Intertwining and Supercuspidal Types for p‐Adic Classical Groups

- Mathematics
- 2001

Let F be a non-archimedean local field of residual characteristic different from 2, and let G be a unitary, symplectic or orthogonal group, considered as the fixed point subgroup in = GL(N,F) of an… Expand

Semisimple strata for p-adic classical groups☆

- Mathematics
- 2002

Let F0 be a non-archimedean local field, of residual characteristic different from 2, and let G be a unitary, symplectic or orthogonal group defined over F0. In this paper, we prove some fundamental… Expand