Related papers: Super-Whittaker vector at c=3/2

This paper is devoted to the phenomenon of superintegrability. This phenomenon is manifested in the existence of a formula for character averages, expressed through the same characters at special points and of its various generalization. In…

In complex vector spaces maximal sets of equiangular lines, known as SICs, are related to real quadratic number fields in a dimension dependent way. If the dimension is of the form $n^2+3$ the base field has a fundamental unit of negative…

We consider a deformation of N=1 supersymmetric gauge theories in four dimensions, which we call the C-deformation, where the gluino field satisfies a Clifford-like algebra dictated by a self-dual two-form, instead of the standard…

In the present paper we construct all typical finite-dimensional representations of the quantum Lie superalgebra $U_{q}[gl(2/2)]$ at generic deformation parameter $q$. As in the non-deformed case the finite-dimensional…

We develop basic constructions of the Baxter operator formalism for the Macdonald polynomials associated with root systems of type A. Precisely we construct a dual pair of mutually commuting Baxter operators such that the Macdonald…

Let $\mathfrak{o}_l$ be a finite principal ideal local ring of length $l$. The degenerate Whittaker space associated with a representation of ${\rm GL}_{2n}(\mathfrak{o}_l)$ is a representation of ${\rm GL}_n(\mathfrak{o}_l)$. For strongly…

Let $G=GL_{n}(F)$ and let $(\pi_{St},V)$ be a (generalized) Steinberg representation of $G$. It is well known that the space of Iwahori fixed vectors in $V$ is one dimensional. The Iwahori Hecke algebra acts on this space via a character.…

The Hamiltonian of the quantum Calogero-Sutherland model of $N$ identical particles on the circle with $1/r^{2}$ interactions has eigenfunctions consisting of Jack polynomials times the base state. By use of the generalized Jack polynomials…

We construct an irrational C_2-cofinite vertex operator algebra associatted to a finite dimensional vector space with a nondegenerate skew-symmetric bilinear form. We also classify its equivalence classes of irreducible modules and…

In this article we begin the study of representations of simple finite-dimensional noncommutative Jordan superalgebras. In the case of degree $\geq 3$ we show that any finite-dimensional representation is completely reducible and, depending…

Let ${\mathfrak{g}}$ be a complex semisimple Lie algebra with Borel subalgebra ${\mathfrak{b}}$ and corresponding nilradical ${\mathfrak{n}}$. We show that singular Whittaker modules $M$ are simple if and only if the space $\hbox{Wh}\,M$ of…

We consider the unital associative algebra $\mathcal{A}$ with two generators $\mathcal{X}$, $\mathcal{Z}$ obeying the defining relation $[\mathcal{Z},\mathcal{X}]=\mathcal{Z}^2+\Delta$. We construct irreducible tridiagonal representations…

Let k be an algebraically closed field of characteristic two. Let R be the ring of Witt vectors of length two over k. We construct a group stack \hat G over k, the metaplectic extension of the Greenberg realization of Sp_{2n}(R). We also…

We begin by reviewing Zhu's theorem on modular invariance of trace functions associated to a vertex operator algebra, as well as a generalisation by the author to vertex operator superalgebras. This generalisation involves objects that we…

The properties of highest-weight representations of the N=2 superconformal algebra in two dimensions can be considerably simplified when re-expressed in terms of relaxed ^sl(2) representations. This applies to the appearance of submodules…

Let $\pi$ be an irreducible cuspidal representation of $\mathrm{GL}_{kn}\left(\mathbb{F}_q\right)$. Assume that $\pi = \pi_{\theta}$, corresponds to a regular character $\theta$ of $\mathbb{F}_{q^{kn}}^{*}$. We consider the twisted Jacquet…

This paper is concerned with the subduction problem of type A quantum Iwahori-Hecke algebras $\mathbb{C} \mathbf{H}(\mathfrak{S}_f,q^2)$ with a real deformation parameter $q$, i.e. the problem of decomposing irreducible representations of…

It has been shown that the Cartan subalgebra of $W_{\infty}$- algebra is the space of the two-variable, definite-parity polynomials. Explicit expressions of these polynomials, and their basic properties are presented. Also has been shown…

As shown by Ashtekar in the mid 80's, general relativity can be extended to incorporate degenerate metrics. This extension is not unique, however, as one can change the form of the hamiltonian constraints and obtain an {\it alternative}…

We consider a general class of Fourier coefficients for an automorphic form on a finite cover of a reductive adelic group ${\bf G}(\mathbb{A}_{\mathbb{K}})$, associated to the data of a `Whittaker pair'. We describe a quasi-order on Fourier…