Related papers: The Character of the Infinite Wedge Representation

In this article, we exploit the theory of graded module category with semi-infinite character developed by Soergel in \cite{Soe} to study representations of the infinite dimensional Lie algebras of vector fields $W(n), S(n)$ and $H(n)$…

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…

We study finite dimensional algebras that appear as fibers of quantum orders over a given point of variety of center. We present the formula for the number of irreducible representations and check it for it for the algebra of twisted…

In general, in gauge field theories, physical observables are represented by gauge-invariant composite operators, such as the electromagnetic current. As we recently demonstrated in the context of the $U\left(1\right)$ and…

We provide new representations for the finite parts at the poles and the derivative at zero of the Barnes zeta function in any dimension in the general case. These representations are in the forms of series and limits. We also give an…

In this paper we study the representation theory for certain ``half lattice vertex algebras.'' In particular we construct a large class of irreducible modules for these vertex algebras. We also discuss how the representation theory of these…

Let G by compact p-adic Lie group and suppose that G is FAb, i.e., that H/[H,H] is finite for every open subgroup H of G. The representation zeta function Z(G,s) encodes the distribution of continuous irreducible complex characters of G.…

We give a functional characterization of a class of quasi-invariant determinantal processes corresponding to projection kernels in terms of de Branges spaces of entire funcitons.

We extend the modular invariance property of the trace functions of vertex operator algebra on the set of irreducible modules (Zhu's theory) to the case of trace functions of intertwining operators.

In this lecture, we survey a number of recent results and developments regarding the representation theory of infinite-dimensional quantum groups (quantum affine algebras and related algebras), as well as their connections with cluster…

We study a fractional differentiation operator for functions on the conjugate space to an infinite extension of a local field of zero characteristic which is a union of an increasing sequence of finite extensions. In particular, a…

We survey some important results concerning the finite--dimensional representations of the loop algebra of a simple complex Lie algebra, and their twisted loop subalgebras. In particular, we review the parametrization and description of the…

We construct symmetric square type $L$-series for vector-valued modular forms transforming under the Weil representation associated to a discriminant form. We study Hecke operators and integral representations to investigate their…

In this paper, we study modular transformation properties of a certain class of functions with indefinite quadratic forms.

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

The aim of this paper is to extend the structure theory for infinitely generated modules over tame hereditary algebras to the more general case of modules over concealed canonical algebras. Using tilting, we may assume that we deal with…

This paper extends previous work on linear correlations of representation functions of positive definite binary quadratic forms to allow indefinite forms.

In this paper, we study the composition operators on an algebra of Dirichlet series, the analogue of the Wiener algebra of absolutely convergent Taylor series, which we call the Wiener-Dirichlet algebra. We study the connection between the…

Physicists showed that the generating function of orbifold elliptic genera of symmetric orbifolds can be written as an infinite product. We show that there exists a geometric factorization on space level behind this infinite product formula…

We study the composition operators on an algebra of Dirichlet series, the analogue of the Wiener algebra of absolutely convergent Taylor series, which we call the Wiener-Dirichlet algebra. The central issue is to understand the connection…