Inspired by Ol′šhanskiĭ’s work, we provide an axiomatic framework to describe certain irreducible unitary representations of non-discrete unimodular totally disconnected locally compact groups. We look at the applications groups automorphisms finite trees and semi-regular right-angled buildings.

It is well known that the category of super Lie groups (SLG) is equivalent to the category of super Harish-Chandra pairs (SHCP). Using this equivalence, we define the category of unitary representations (UR’s) of a super Lie group. We give an extension of the classical inducing construction and Mackey imprimitivity theorem to this setting. We use our results to classify the irreducible unitary ...

It is well known that the category of super Lie groups (SLG) is equivalent to the category of super Harish-Chandra pairs (SHCP). Using this equivalence, we define the category of unitary representations (UR's) of a super Lie group. We give an extension of the classical inducing construction and Mackey imprimitivity theorem to this setting. We use our results to classify the irreducible unitary ...

For K/F a quadratic extension of p-adic fields, let σ be the conjugation relative to this extension, and ηK/F be the character of F ∗ with kernel norms of K. If π is a smooth irreducible representation of GL(n,K), and χ a character of F , the dimension of the space of linear forms on its space, which transform by χ under GL(n, F ) (with respect to the action [(L, g) 7→ L ◦ π(g)]) , is known to ...

Let F be a finite field or a local field of any characteristic. If A is a finite dimensional associative nilpotent algebra over F , the set 1 +A of all formal expressions of the form 1 +x, where x ∈ A, is a locally compact group with the topology induced by the standard one on F and the multiplication (1 + x) · (1 + y) = 1 + (x + y + xy). We prove a result conjectured by E. Gutkin in 1973: ever...

In this article, we introduce monomial irreducible representations of the special linear Lie algebra $sln$. We will show that this kind of representations have bases for which the action of the Chevalley generators of the Lie algebra on the basis elements can be given by a simple formula.