Related papers: A note on representations of $SL_n$

In this paper we study irreducible unitary representations of GL(n,R) and prove a number of results. Our first result establishes a precise connection between the annihilator of a representation and the existence of degenerate Whittaker…

Multidimensional contractions of irreducible representations of the Cayley-Klein unitary algebras in the Gel'fand-Zetlin basis are considered. Contracted over different parameters, algebras can turn out to be isomorphic. In this case method…

This paper describes finite dimensionall irreducible representations of both twisted and untwisted Cartan map Lie superalgebras.

We study representations of GL(n) appearing as quotients of a tensor of exceptional representations, in the sense of Kazhdan and Patterson. Such representations are called distinguished. We characterize distinguished principal series…

We study the complex irreducible representations of special linear, symplectic, orthogonal and unitary groups over principal ideal local rings of length two. We construct a canonical correspondence between the irreducible representations of…

We give new, explicit and asymptotically sharp, lower bounds for dimensions of irreducible modular representations of finite symmetric groups.

We consider two bases for an arbitrary finite dimensional irreducible representation of a complex special linear Lie algebra: the classical Gelfand-Tsetlin basis and the relatively new Chari-Loktev basis. Both are parametrized by the set of…

We present an application of Hodge theory towards the study of irreducible unitary representations of reductive Lie groups. We describe a conjecture about such representations and discuss some progress towards its proof.

Using the entropic inequalities for Shannon and Tsallis entropies new inequalities for some classical polynomials are obtained. To this end, an invertible mapping for the irreducible unitary representation of groups $SU(2)$ and $SU(1,1)$…

Gelfand-Graev characters and their degenerate counterparts have an important role in the representation theory of finite groups of Lie type. Using a characteristic map to translate the character theory of the finite unitary groups into the…

Suppose G is a real reductive Lie group in Harish-Chandra's class. We propose here a structure for the set \Pi_u(G) of equivalence classes of irreducible unitary representations of G. (The subscript u will be used throughout to indicate…

We begin a systematic study of unitary representations of minimal $W$-algebras. In particular, we classify unitary minimal $W$-algebras and make substantial progress in classification of their unitary irreducible highest weight modules. We…

The problem of computing the characters of the finite dimensional irreducible representations of the Lie superalgebra $\mathfrak{gl}(m|n)$ over $\C$ was solved a few years ago by V. Serganova. In this article, we present an entirely…

In the paper we consider a realization of a finite dimensional irreducible representation of the Lie algebra $\mathfrak{gl}_n$ in the space of functions on the group $GL_n$. It is proved that functions corresponding to Gelfand-Tsetlin…

The aim of this note is to provide a self-contained classification of the irreducible representations of generalised Kac--Paljutkin Hopf algebras, recently introduced by the second author.

We give presentations, in terms of the generators and relations, for the reflection equation algebras of type $GL_n$ and $SL_n$, i.e., the covariantized algebras of the dual Hopf algebras of the small quantum groups of $\mathfrak{gl}_n$ and…

The new approach to the theory of complex representrations of the finite symmetric groups which based on the notions of Coxeter generators., Gelfand-Zetlin algebras, Hecke algebra, Young-Jucys-Murphi generators and which hardly used…

The SU(2) TQFT representation of the mapping class group of a closed surface of genus g, at a root of unity of prime order, is shown to be irreducible. Some examples of reducible representations are also given.

We give parameterizations of the irreducible representations of finite groups of Lie type in their defining characteristic.

An irreducible representation of a reductive Lie algebra, when restricted to a Cartan subalgebra, decomposes into weights with multiplicity. The first part of this paper outlines a procedure to compute symmetric polynomials (e.g., power…