Related papers: Representations of McLain groups
A parametrization of irreducible unitary representations associated with the regular adjoint orbits of a hyperspecial compact subgroup of a reductive group over a non-dyadic non-archimedean local filed is presented. The parametrization is…
The decomposition matrix of a finite group in prime characteristic p records the multiplicities of its p-modular irreducible representations as composition factors of the reductions modulo p of its irreducible representations in…
Several recent problems in the representation theory of finite groups require determining whether certain characters of almost simple groups belong to the principal block. Since the values of these characters are not yet known, we employ…
We show that for any finite-dimensional algebra $\Lambda$ of infinite representation type, over a perfect field, there is a bounded principal ideal domain $\Gamma$ and a representation embedding from $\Gamma -$mod into $\Lambda -$mod. As an…
In this paper we give a small review of some recent results of elementary equivalence of linear and algebraic groups and our last new results of elementary equivalence of categories of modules, endomorphism rings of modules, lattices of…
We study finiteness conditions on large tilting modules over arbitrary rings. We then turn to a hereditary artin algebra R and apply our results to the (infinite dimensional) tilting module L that generates all modules without preprojective…
In this paper we study algebras of modular forms on unitary groups of signature $(n,1)$. We give a necessary and sufficient condition for an algebra of unitary modular forms to be free in terms of the modular Jacobian. As a corollary we…
We establish a canonical basis character formula for the irreducible modules in arbitrary parabolic BGG-type categories, including the category of finite-dimensional modules, for finite $W$-superalgebras of type $A$. These categories…
We investigate the permutation modules associated to the set of $k$-dimensional faces of the hyperoctahedron in dimension $n$, denoted $H^{n}.$ For any $k\leq n$ such a module can be defined over an arbitrary field $F$, it is called a face…
For an arbitrary infinite field k of characteristic p > 0, we describe the structure of a block of the algebraic monoid M_n(k) (all n x n matrices over k), or, equivalently, a block of the Schur algebra S(n,p), whose simple modules are…
In this article, we study the representation theory of shifted super Yangians and finite $W$-superalgebras of type A. A criterion for the finite dimensionality of irreducible modules is obtained in the standard parity case. Furthermore, we…
In this paper, we study the category of modules over the Smith algebra which are free of finite rank over the unital polynomial subalgebra generated by the Cartan element $h$ and obtain families of such simple modules of arbitrary rank. In…
We show that the mirabolic quantum group $MU(n)$ is a comodule algebra over the quantized enveloping algebra $U_v(\mathfrak{sl}_n)$, and use this structure to give a complete classification of its finite dimensional representations. In…
In this paper, we classify irreducible modules for loop extended Witt algebras with finite dimensional weight spaces. They turn out to be either modules with uniformly bounded weight spaces or highest weight modules. We further prove that…
We prove that the problems of representing a finite ordered complemented semigroup or finite lattice-ordered semigroup as an algebra of binary relations over a finite set are undecidable. In the case that complementation is taken with…
Let $p$ be a prime. Given a split semisimple group scheme $G$ over a normal integral domain $R$ which is a faithfully flat $\mathbb Z_{(p)}$-algebra, we classify all finite dimensional representations $V$ of the fiber $G_K$ of $G$ over…
Finite dimensional modular Lie superalgebras over algebraically closed fields with indecomposable Cartan matrices are classified under some technical, most probably inessential, hypotheses. If the Cartan matrix is invertible, the…
Infinite dimensional representations of the real form U_q(u_{n,1}) of the Drinfeld--Jimbo algebra U_q(gl_{n+1}) are defined. The principal series of representations of U_q(u_{n,1}) is studied. Intertwining operators for pairs of the…
This paper is concerned with absolutely irreducible quasisimple subgroups $G$ of a finite general linear group $GL_d(\mathbb{F}_q)$ for which some element $g\in G$ of prime order $r$, in its action on the natural module…
In paper, we study the representation theory of super $W(2,2)$ algebra ${\mathfrak{L}}$. We prove that ${\mathfrak{L}}$ has no mixed irreducible modules and give the classification of irreducible modules of intermediate series. We…