Endo-classes for p-adic classical groups

Research paper by Robert Kurinczuk, Daniel Skodlerack, Shaun Stevens

Indexed on: 08 Nov '16Published on: 08 Nov '16Published in: arXiv - Mathematics - Representation Theory


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. This completes work of the third author who showed that every irreducible cuspidal representation of such a classical group is compactly induced from a cuspidal type, now giving a classification of irreducible cuspidal representations of classical groups in terms of cuspidal types. Our approach is to completely understand the intertwining of the so-called self dual semisimple characters, which form \emph{the} fundamental step in the construction. To this aim, we generalise Bushnell--Henniart's theory of endo-class for simple characters of general linear groups to a theory for self dual semisimple characters of classical groups, and introduce (self dual) endo-parameters which parametrise intertwining classes of (self dual) semisimple characters.