Local newforms for the general linear groups over a non-archimedean local field

Remark on Representation Theory of General Linear Groups over a Non-archimedean Local Division Algebra

In this paper we give a simple (local) proof of two principal results about irreducible tempered representations of general linear groups over a non-archimedean local division algebra A. We give a proof of the parameterization of the irreducible square integrable representations of these groups by segments of cuspidal representations, and a proof of the irreducibility of the tempered parabolic ...

Kirillov Theory for Gl2( ) Where Is a Division Algebra over a Non-archimedean Local Field

On the Classification of Rank 1 Groups over Non-archimedean Local Fields

We outline the classification of K-rank 1 groups over non-archimedean local fields K up to strict isogeny, as in [Ti1] and [Ti2]. We outline the classification of absolutely simple algebraic groups over non-archimedean local fields, up to strict isogeny. This is classical, and accounts of it have been written by Tits ([Ti1], [Ti2]) and Satake ([Sa]). Tits compiled tables of ‘admissible indices’...

ON NILPOTENT ORBITS OF SLn AND Sp2n OVER A LOCAL NON-ARCHIMEDEAN FIELD

We relate the partition-type parametrization of rational (arithmetic) nilpotent adjoint orbits of the classical groups SLn and Sp2n over local non-Archimedean fields with a parametrization, introduced by DeBacker in 2002, which uses the associated Bruhat-Tits building to relate the question to one over the residue field.

Character Sheaves of Algebraic Groups Defined over Non-archimedean Local Fields

This paper concerns character sheaves of connected reductive algebraic groups defined over non-Archimedean local fields and their relation with characters of smooth representations. Although character sheaves were devised with characters of representations of finite groups of Lie type in mind, character sheaves are perfectly well defined for reductive algebraic groups over any algebraically clo...