Related papers: Action of Virasoro operators on Hall-Littlewood po…

An observation on Hall-Littlewood polynomials.

A formula for Schur $Q$-functions is presented which describes the action of the Virasoro operators. For a strict partition, we prove a concise formula for $L_{-k}Q_{\lambda}$, where $L_{-k}$ $(k\geq 1)$ is the Virasoro operator.

We obtain explicit expressions for differential operators defining the action of the Virasoro algebra on the space of univalent functions. We also obtain an explicit Taylor decomposition for Schwarzian derivative and a formula for the…

We prove the existence of Hall polynomials for $x^2$-bounded invariant subspaces of nilpotent linear operators.

The aim of this note is to give some factorization formulas for different versions of the Macdonald polynomials when the parameter t is specialized at roots of unity, generalizing those existing for Hall-Littlewood functions.

We extend our previous work on Poisson-like formulas for subresultants in roots to the case of polynomials with multiple roots in both the univariate and multivariate case, and also explore some closed formulas in roots for univariate…

We use Rogers-Szego polynomials to unify some well-known identities for Hall-Littlewood symmetric functions due to Macdonald and Kawanaka.

Shifting by \pm 1 powers sums: p_i \to p_i \pm 1 induces a transformation on symmetric functions that we detail in the case of Hall-Littlewood polynomials. By iteration, this gives a description of these polynomials in terms of plane…

Quantum algebra of differential operators are studied

We show that Narayana polynomials are a specialization of row Hall-Littlewood symmetric functions. Using lambda-ring calculus, we generalize to Narayana polynomials the formulas of Koshy and Jonah for Catalan numbers.

We give a formula for pushing forward the classes of Hall-Littlewood polynomials in Grassmann bundles, generalizing Gysin formulas for Schur S- and Q-functions.

Hall-Littlewood functions indexed by rectangular partitions, specialized at primitive roots of unity, can be expressed as plethysms. We propose a combinatorial proof of this formula using A. Schilling's bijection between ribbon tableaux and…

In this paper, extensions of nonunitary rational Virasoro vertex operator algebras corresponding to some exceptional modular invariants are constructed. The uniqueness of these extensions is also established.

We show the existence of Hall polynomials for representation-finite cluster-tilted algebras.

Vertex operators for the deformed Virasoro algebra are defined, their bosonic representation is constructed and difference equation for the simplest vertex operators is described.

In this paper, we study properties of polynomials over division rings. Moreover, we present formulas for finding roots of some polynomials

We extend the authors' previous work on Wiener-Wintner double recurrence theorem to the case of polynomials.

We study the Virasoro constraints for moduli spaces of representations of quiver with relations by Joyce's vertex algebras. Using the framed Virasoro constraints, we construct a representation of half of the Virasoro algebra on the…

In this paper we obtain quite general and definitive forms for Hardy-Littlewood type inequalities. Moreover, when restricted to the original particular cases, our approach provides much simpler and straightforward proofs and we are able to…

In this note, we present a formula for the action of the primitive Milnor operations on generators of algebra of invariants of the general linear group $GL_n=GL(n, \mathbb F_p)$ in the polynomial algebra $P_n= \mathbb…