Related papers: Vertex operators arising from Jacobi-Trudi identit…

The problem of constructing twisted modules for a vertex operator algebra and an automorphism has been solved in particular in two contexts. One of these two constructions is that initiated by the third author in the case of a lattice…

Connection, torsion and curvature are introduced for general (local) Leibniz algebroids. Generalized Bismut connection on $TM \oplus \Lambda^{p} T^{\ast}M$ is an example leading to a scalar curvature of the form $R + H^2$ for a closed…

We study non-associative twisted group algebras over $(\Z_2)^n$ with cubic twisting functions. We construct a series of algebras that extend the classical algebra of octonions in the same way as the Clifford algebras extend the algebra of…

We study relationships between spinor representations of certain Lie algebras and Lie superalgebras of differential operators on the circle and values of $\zeta$--functions at the negative integers. By using formal calculus techniques we…

In this paper, we construct Laplace-Beltrami operators associated with arbitrary Riemannian metrics on noncommutative tori of any dimension. These operators enjoy the main properties of the Laplace-Beltrami operators on ordinary Riemannian…

The multi-indexed Jacobi polynomials are the main part of the eigenfunctions of exactly solvable quantum mechanical systems obtained by certain deformations of the P\"oschl-Teller potential (Odake-Sasaki). By fine-tuning the parameter(s) of…

We discuss a recent proof by the author of a general version of the Verlinde conjecture in the framework of vertex operator algebras and the application of this result to the construction of modular tensor tensor category structure on the…

We prove an identity on a graph analogous to Bochner's identity on a Riemannian manifold. An auxiliary graph called the complete tangent graph intervenes in the term corresponding to Ricci curvature.

The affine vertex operator algebras for $\mathfrak{sl}_2$ and the Virasoro minimal models are related by Drinfeld-Sokolov reduction and by the Goddard-Kent-Olive coset construction. In this work, we propose another connection based on…

This paper is a contribution to the study of the relations between special functions, Lie algebras and rigged Hilbert spaces. The discrete indices and continuous variables of special functions are in correspondence with the representations…

We study the covariant derivatives of an eigenfunction for the Laplace-Beltrami operator on a complete, connected Riemannian manifold with nonzero constant sectional curvature. We show that along every parallel tensor, the covariant…

Jacobi/Poisson algebras are algebraic counterparts of Jacobi/Poisson manifolds. We introduce representations of a Jacobi algebra $A$ and Frobenius Jacobi algebras as symmetric objects in the category. A characterization theorem for…

We present a formulas to add a row or a column to the power, monomial, forgotten, Schur, homogeneous and elementary symmetric functions. As an application of these operators we show that the operator that adds a column to the Schur…

We define a number of related combinatorial objects, each of which possesses a surprising symmetry. We include several applications such as a combinatorial explanation for certain fixed points of the involution $\omega$ on the ring of…

Let $X$ be an Archimedean vector lattice. We investigate subalgebras of $\mathscr{L}(X)$ consisting of regular operators that contain all rank-one operators of the form $a \otimes \varphi_b$, where $a$ and $b$ are atoms of $X$ and…

The aim of this work is to report on several ladder operators for generalized Zernike polynomials which are orthogonal polynomials on the unit disk $\mathbf{D}\,=\,\{(x,y)\in \mathbb{R}^2: \; x^2+y^2\leqslant 1\}$ with respect to the weight…

We study the properties of shifted vertex operator algebras, which are vertex algebras derived from a given theory by shifting the conformal vector. In this way, we are able to exhibit large numbers of vertex operator algebras which are…

We study the Gaberdiel-Goddard spaces of systems of correlation functions attached to an affine Kac-Moody Lie algebra $\gh$. We prove that these spaces are isomorphic to the spaces of coinvariants with respect to certain subalgebras of…

We study the $t$-Schur measure on partitions, defined by $ \mathbb{P}(\lambda)=Z^{-1}S_\lambda(x;t)s_\lambda(y) $, where $S_\lambda(x;t)$ denotes the $t$-Schur symmetric functions and $s_\lambda(y)$ the ordinary Schur functions, and $Z$ is…

In this paper, a link between $q$-difference equations, Jacobi operators and orthogonal polynomials is given. Replacing the variable $x$ by $ q^{-n}$ in a Sturm-Liouville $q$-difference equation we discovered the Jacobi operator. With…