Related papers: Weyl's Character Formula for $SU(3)$ - A Generatin…

In a noncommutative algebra there is no canonical way to express elements in univalent way, which is often called "ordering problem". In this note we give product formula of the Weyl algebra in generic ordered expression. In particular, the…

The construction of the fusion ring of a quasi-rational CFT based on $\hat{sl}(3)_k$ at generic level $k\not \in {\Bbb Q}$ is reviewed. It is a commutative ring generated by formal characters, elements in the group ring ${\Bbb…

This paper uses deformed coherent states, based on a deformed Weyl-Heisenberg algebra that unifies the well-known SU(2), Weyl-Heisenberg, and SU(1,1) groups, through a common parameter. We show that deformed coherent states provide the…

We obtain a general expression for a Wigner transform (Wigner function) on symmetric spaces of non-compact type and study the Weyl calculus of pseudodifferential operators on them.

We introduce generalized global Weyl modules and relate their graded characters to nonsymmetric Macdonald polynomials and nonsymmetric $q$-Whittaker functions. In particular, we show that the series part of the nonsymmetric $q$-Whittaker…

We use Seiberg--Witten-like relations in the topological recursion framework to obtain virtual Euler characteristics for uni- and multicellular maps for ensembles of classic orthogonal polynomials and for ensembles related to nonorientable…

In this paper I present a new and unified method of proving character formulas for discrete series representations of connected Lie groups by applying a Chern character-type construction to the matrix factorizations of [FT] and [FHT3]. In…

The generalized Kazhdan-Lusztig polynomials for the finite dimensional irreducible representations of the general linear superalgebra are computed explicitly. Using the result we establish a one to one correspondence between the set of…

Let f be a Hecke-Maass or holomorphic primitive cusp form for $SL(2,\mathbb{Z})$ with Fourier coefficients $\lambda_{f}(n)$. Let $\chi$ be a primitive Dirichlet character of modulus p, where p is a prime number. In this article we prove the…

Many combinatorial generating functions can be expressed as combinations of symmetric functions, or extracted as sub-series and specializations from such combinations. Gessel has outlined a large class of symmetric functions for which the…

We construct a Weyl x SU(2)_L x U(1)_Y invariant theory by extending four-dimensional Weyl quadratic gravity with Weyl-invariant scalar, fermion, Yukawa and gauge sectors. The quadratic structure (R^tilde - mu^2 |phi|^2)^2 allows the Weyl…

We construct and normalise intertwining operators at the level of Hilbert modules describing the principal series of SL(2). Normalisation is achieved through the use of a Fourier transform defined on some homogenous space and twisted by a…

General formulas for the scalar modes a_i and a^i_D in the Seiberg-Witten SU(N) setting are derived in the cases with and without massive hypermultiplets. Subsequently these formulas are applied in a study of the SU(3) Argyres-Douglas…

We construct a new dilaton Weyl multiplet for $\mathcal{N}=3$ conformal supergravity in four dimensions. The R-symmetry realized on this dilaton Weyl multiplet is $SU(2) \times U(1) \times U(1)$. The construction follows a two-step…

In the first part, we construct a new isomorphism between the endomorphism algebra of an induced cuspidal character sheaf and the group algebra of the relative Weyl group involved. We show it differs from the isomorphism of Lusztig by a…

We show how to represent a class of expressions involving discrete sums over partitions as matrix models. We apply this technique to the partition functions of 2* theories, i.e. Seiberg-Witten theories with the massive hypermultiplet in the…

We identify the spectral curve of pure gauge SU(2) Seiberg-Witten theory with the Weierstrass curve $\mathbbm{C}/L \ni z \mapsto (1,\wp(z),\wp(z)')$ and thereby obtain explicitely a modular form from which the moduli space parameter $u$ and…

A method for successive synthesis of the Weyl matrix on the square lattice is proposed. It allows one to compute the Weyl matrix of a large graph by adding new edges and solving elementary systems of linear algebraic equations at each step.…

Sato introduced the tau-function to describe solutions to a wide class of completely integrable differential equations. Later Segal-Wilson represented it in terms of the relevant integral operators on Hardy space of the unit disc. This…

Let V be a finite dimensional vector space over the field with two elements with a given nondegenerate symplectic form. Let [V] be the vector space of complex valued functions on V and let [V]_Z be the subgroup of [V] consisting of integer…