Related papers: On Mackey Decomposition for locally profinite grou…
We prove a Mackey formula for representations of finite groups of Lie type, in the case where the groups come from disconnected reductive groups.
We develop the theory of Mackey profunctors, a version of Mackey functors for profinite groups.
We define and investigate the concept of the groupoid representation induced by a representation of the isotropy subgroupoid. Groupoids in question are locally compact transitive topological groupoids. We formulate and prove the…
We survey several notions of Mackey functors and biset functors found in the literature and prove some old and new theorems comparing them. While little here will surprise the experts, we draw a conceptual and unified picture by making…
We generalize the Cauchy-Davenport theorem to locally compact groups.
In this work we extend the Mackey's theory of induced unitary representations on a wide class of Krein-isometric induced representations in Krein spaces. The subgroup theorem and the Kronecker product theorem are shown to be valid for the…
This paper gives a $p$-adic analogue of the Mackey theory, which relates representations of a group of type $G=H\times_{t} A $ to systems of imprimitivity.
For half a century, Mackey and Green functors have been successfully used to model the induction and restriction maps which are ubiquitous in the representation theory of finite groups. In the examples, the latter maps are typically…
A general Mackey type decomposition for representations of semisimple Hopf algebras is investigated. We show that such a decomposition occurs in the case that the module is induced from an arbitrary Hopf subalgebra and it is restricted back…
Sp\"ath showed that the Alperin-McKay conjecture in the representation theory of finite groups holds if the so-called inductive Alperin-McKay condition holds for all finite simple groups. In a previous article, we showed that the…
Given a real reductive group Lie group $G_\mathbb{R}$, the Mackey analogy is a bijection between the set of irreducible tempered representations of $G_\mathbb{R}$ and the set of irreducible unitary representations of its Cartan motion…
The representation theory for categorical groups is constructed. Each categorical group determines a monoidal bicategory of representations. Typically, these categories contain representations which are indecomposable but not irreducible. A…
The aim of the present paper is to expose two contributions of Mackey, together with a more recent result of Kawanaka and Matsuyama, generalized by Bump and Ginzburg, on the representation theory of a finite group equipped with an…
We verify the inductive McKay condition for simple groups of Lie type C, namely finite projective symplectic groups. This contributes to the program of a complete proof of the McKay conjecture for all finite groups via the reduction theorem…
We give a survey of recent developments in the investigation of the various local-global conjectures for representations of finite groups.
A survey of recent results about profinite groups, and results about infinite and finite groups where the theory of profinite groups plays a leading role.
We give some background on uniform pro-p groups and the model theory of profinite NIP groups.
The paper studies weak Paley-Wiener properties for group extensions by use of Mackey's theory. The main theorem establishes sufficient conditions on the dual action to ensure that the group has the weak Paley-Wiener property. The theorem…
In this paper we study a natural decomposition of $G$-equivariant $K$-theory of a proper $G$-space, when $G$ is a Lie group with a compact normal subgroup $A$ acting trivially. Our decomposition could be understood as a generalization of…
Recently there has been a lot of research and progress in profinite groups. We survey some of the new results and discuss open problems. A central theme is decompositions of finite groups into bounded products of subsets of various kinds…