相关论文: Description of unitary representations of the grou…

We study a coarse moduli space of irreducible representations of the group of unipotent matrices of order $\mathbb{4}$ over the ring of integers which have finite weight. All such representations are known to be monomial. To describe a…

We introduce an infinite-dimensional $p$-adic affine group and construct its irreducible unitary representation. Our approach follows the one used by Vershik, Gelfand and Graev for the diffeomorphism group, but with modifications made…

We classify the automorphic representations (over number fields) and the irreducible admissible representations (over local fields) of unitary groups which are not quasi-split, under the assumption that the same is known for quasi-split…

Let $A$ be a ring with $1\neq 0$, not necessarily finite, endowed with an involution~$*$, that is, an anti-automorphism of order $\leq 2$. Let $H_n(A)$ be the additive group of all $n\times n$ hermitian matrices over $A$ relative to $*$.…

This paper contains a complete description of classes of the unitary equivalence of the admissible representations of infinite-dimensional classic matrix groups paper.

We give a classification of irreducible admissible modulo $p$ representations of a split $p$-adic reductive group in terms of supersingular representations. This is a generalization of a theorem of Herzig.

Let O be a complete discrete valuation domain with finite residue field. In this paper we describe the irreducible representations of the groups Aut(M) for any finite O-module M of rank two. The main emphasis is on the interaction between…

In this paper we study certain category of smooth modules for reductive $p$--adic groups analogous to the usual smooth complex representations but with the field of complex numbers replaced by a $\mathbb Q$--algebra. We prove some…

We classify globally irreducible representations of alternating groups and double covers of symmetric and alternating groups. In order to achieve this classification we also completely characterise irreducible representations of such groups…

We obtain a description of the irreducible representation algebra of the alternating group of degree four over the ring of 2-adic integers.

In this paper we determine the representation type of some algebras of infinite matrices continuously controlled at infinity by a compact metrizable space. We explicitly classify their finitely presented modules in the finite and tame…

Let $G$ be an infinite-dimensional real classical group containing the complete unitary group (or complete orthogonal group) as a subgroup. Then $G$ generates a category of double cosets (train) and any unitary representation of $G$ can be…

We define basic notions in the category of conic representations of a topological group and prove elementary facts about them. We show that a conic representation determines an ordinary dynamical system of the group together with a…

We classify the irreducible representations of smooth, connected affine algebraic groups over a field, by tackling the case of pseudo-reductive groups. We reduce the problem of calculating the dimension for pseudo-split pseudo-reductive…

We construct irreducible unitary representations of a finitely generated free group which are weakly contained in the left regular representation and in which a given linear combination of the generators has an eigenvalue. When the…

We enumerate the number of complex irreducible representations of each degree of general unitary groups of degree 4 over principal ideal rings of length 2.

Let $G$ be a locally compact totally disconnected topological group. Under a necessary mild assumption, we show that the irreducible unitary representations of $G$ are uniformly admissible if and only if the irreducible smooth…

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…

We describe isomorphisms of groups of several periodic infinite matrices and isomorphisms of groups of invertible elements of unital locally matrix algebras.

Given a quaternionic form G of a p-adic classical group (p odd) we classify all cuspidal irreducible representations of G with coefficients in an algebraically closed field of characteristic different from p. We prove two theorems: At…