Related papers: On Projective Representations of Special p-groups

Let $G$ be a real compact Lie group, such that $G=G^0\rtimes C_2$, with $G^0$ simple. Here $G^0$ is the connected component of $G$ containing the identity and $C_2$ is the cyclic group of order $2$. We give a criterion for whether an…

The representation dimension of a finite group G is the smallest positive integer m for which there exists an embedding of G in GL_m(C). In this paper we find the largest value of representation dimensions, as Granges over all groups of…

We study finite dimensional representations of the projective modular group. Various explicit dimension formulas are given.

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.

For a prime $p,$ let $\mathbb{F}_q$ be a finite extension of $\mathbb{F}_p.$ The restriction of an irreducible mod $p$ representation of $\text{GL}_2(\mathbb{F}_q)$ to its subgroup $\text{GL}_2(\mathbb{F}_p)$ can be seen as a tensor product…

A complex irreducible character of a finite group G is said to be p-constant, for some prime p dividing the order of G, if it takes constant value at the set of p-singular elements of G. In this paper we classify irreducible p-constant…

Minimal representations of a real reductive group G are the `smallest' irreducible unitary representations of G. We discuss special functions that arise in the analysis of L^2-model of minimal representations.

Let W be a Weyl group. We define a class of irreducible representations of W that we call antispecial. They are in bijection with the constructible representations of W. We define an oriented graph structure on the set of antispecial…

We give an elementary analysis of the multiplicator group of the Galilei group in 1+2 dimensions $G^{\uparrow}_{+}$. For a non-trivial multiplicator we give a list of all the corresponding projective unitary irreducible representations of…

We investigate the rate of growth of the function of n which counts the number of complex irreducible representations of a fixed group of degree less than or equal to n. The emphasis is on linear groups, especially compact real and p-adic…

We consider the capability of $p$-groups of class two and odd prime exponent. The question of capability is shown to be equivalent to a statement about vector spaces and linear transformations, and using the equivalence we give proofs of…

We calculate extensions between certain irreducible admissible representations of p-adic groups.

Methods are developed for systematically constructing the finite dimensional irreducible representations of the super Yangian Y(gl(M|N)) associated with the Lie superalgebra gl(M|N). It is also shown that every finite dimensional…

Continuing earlier work, we show how to realize irreducible finite-dimensional representations of the complex group of type $G_2$ via tableaux, along the way exhibiting explicit generators of the defining ideal of the flag variety

We classify irreducible representations of the special linear groups in positive characteristic with small weight multiplicities with respect to the group rank and give estimates for the maximal weight multiplicities. For the natural…

We characterize finite-dimensional thick representations over ${\Bbb C}$ of connected complex semi-simple Lie groups by irreducible representations which are weight multiplicity-free and whose weight posets are totally ordered sets.…

This paper is a sequel to arXiv:1401.6321. We define and study representation categories based on Deligne categories Rep(GL_t), Rep(O_t), Rep(Sp_2t), where t is any (non-integer) complex number. Namely, we define complex rank analogs of the…

Let $p$ be a fixed prime number. The main purpose of this paper is to introduce the notion of \textit{irreducible} $p$-local compact group, which provides a first reduction towards a classification of all $p$-local compact groups. In order…

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 prove that any connected reductive group of semisimple $F$-rank 1 over a $p$-adic field admits an irreducible admissible supersingular mod-$p$ representation. This establishes one of the missing cases in Vign\'eras' existence proof for…