Related papers: Special Functions in Minimal Representations

To a finite group $G$, one can associate several notions of dimensions (or degrees). In this survey, we attempt to bring together some of the notions of dimensions or degrees defined using representations of the group in General Linear…

In this paper we study the minimal faithful permutation representations of $SL_n(\mathbb F_q)$ and $GL_n(\mathbb F_q)$.

Representing spectral densities, real-frequency, and real-time Green's functions of continuous systems by a small discrete set of complex poles is an ubiquitous problem in condensed matter physics, with applications ranging from quantum…

We study irreducible restrictions from modules over alternating groups to subgroups. We get reduction results which substantially restrict the classes of subgroups and modules for which this is possible. This is known when the…

Let G be the real points of a simply connected, semisimple, simply laced complex Lie group, and let \tilde{G} be the nonlinear double cover of G. We discuss a set of small genuine irreducible representations of \tilde{G} which can be…

Let X = S \oplus G, where S is a countable abelian semigroup and G is a countably infinite abelian group such that {2g : g in G} is infinite. Let pi: X \to G be the projection map defined by pi(s,g) = g for all x =(s,g) in X. Let f:X \to…

Let X be a smooth projective variety of dimension n on which a simple Lie group G acts regularly and non trivially. Then X is not minimal in the sense of the Minimal Model Program. In the paper we work out a classification of X via 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 wish to understand how irreducible representations of a group G behave when restricted to a subgroup G' (the branching problem). Our primary concern is with representations of reductive Lie groups, which involve both algebraic and…

In the paper we study irreducible representations of some nilpotent groups of finite abelian total rank. The main result of the paper states that if a torsion-free minimax group $G$ of nilpotency class 2 admits a faithful irreducible…

We study unitary representations of semidirect products of a compact quantum group with a finite group. We give a classification of all irreducible unitary representations, a description of the conjugate representation of irreducible…

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.

The main result of this paper is the classification of the real irreducible representations of compact Lie groups with vanishing homogeneity rank.

We study the minimal unitary representations of noncompact exceptional groups that arise as U-duality groups in extended supergravity theories. First we give the unitary realizations of the exceptional group E_{8(-24)} in SU*(8) as well as…

We characterize the finite groups of minimal order that admit an irreducible complex character of degree $p$ or $p^2$, where $p$ is a prime.

This paper proposes a new approach to deriving a finite particle content, suitable for the construction of a gauge theory. Specifically, the outlined construction generates a finite set of irreducible gauge representations, which are…

Representations of Quantum Groups U_q (g_n), g_n any semi simple Lie algebra of rank n, are constructed from arbitrary representations of rank n-1 quantum groups for q a root of unity. Representations which have the maximal dimension and…

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…

We introduce the representation category $\mathscr{C}({\bf G})$ for a connected reductive algebraic group ${\bf G}$ which is defined over a finite field $\mathbb{F}_q$ of $q$ elements. We show that this category has many good properties for…

Let $G$ be the $F$-points of a connected reductive group over a non-archimedean local field $F$ of residue characteristic $p$ and $R$ be a commutative ring. Let $P=LU$ be a parabolic subgroup of $G$ and $Q$ be a parabolic subgroup of $G$…