Related papers: Virasoro Action on the $Q$-Functions
An algebraic iterative formula for the spin Kostka-Foulkes polynomial $K^-_{\xi\mu}(t)$ is given using vertex operator realizations of Hall-Littlewood symmetric functions and Schur's Q-functions. Based on the operational formula, more…
Fourier expansion of the integrand in the path integral formula for the partition function of quantum systems leads to a deterministic expression which, though still quite complex, is easier to process than the original functional integral.…
We consider the Schr\"odinger operators which are constructed from the $\lambda$-opers corresponding to solutions of the $\widehat{\mathfrak{sl}}_2$ Gaudin Bethe Ansatz equations. We define and study the connection coefficients called the…
We study the Grushin operators acting on $\mathbb{R}^{d_1}_x \times \mathbb{R}^{d_2}_t$ and defined by the formula \begin{equation*}…
We give a Littlewood-Richardson type rule for expanding the product of a row-strict quasisymmetric Schur function and a symmetric Schur function in terms of row-strict quasisymmetric Schur functions. This expansion follows from several new…
In this article we will derive a combinatorial formula for the partition function p(n). In the second part of the paper we will establish connection between partitions and q-binomial coefficients and give new interpretation for q-binomial…
We discuss shear viscosity of the quark matter by using Kubo formula. The shear viscosity is calculated in the framework of the quasi-particle RPA for the Nambu-Jona-Lasinio model. We obtain a formula that the shear viscosity is expressed…
Specializations of Schur functions are exploited to define and evaluate the Schur functions s_\lambda[\alpha X] and plethysms s_\lambda[\alpha s_\nu(X))] for any \alpha - integer, real or complex. Plethysms are then used to define pairs of…
The concept of $\lambda$-differential operators is a natural generalization of differential operators and difference operators. In this paper, we determine the $\lambda$-differential Lie algebraic structure on the Witt algebra and the…
We obtain general identities for the product of two Schur functions in the case where one of the functions is indexed by a rectangular partition, and give their t-analogs using vertex operators. We study subspaces forming a filtration for…
The $q$-Whittaker function $W_\lambda(\mathbf{x};q)$ associated to a partition $\lambda$ is a $q$-analogue of the Schur function $s_\lambda(\mathbf{x})$, and is defined as the $t=0$ specialization of the Macdonald polynomial…
We show that the shifted rank, or srank, of any partition $\lambda$ with distinct parts equals the lowest degree of the terms appearing in the expansion of Schur's $Q_{\lambda}$ function in terms of power sum symmetric functions. This gives…
Littlewood-Richardson rule gives the decomposition formula for the multiplication of two Schur functions, while the decomposition formula for the multiplication of two Hall-Littlewood functions or two universal characters is also given by…
An identity is derived expressing Schur functions as sums over products of pairs of Schur $Q$-functions, generalizing previously known special cases. This is shown to follow from their representations as vacuum expectation values (VEV's) of…
We classify quadratic SL(2,K)- and sl(2,K)-modules by crude computation, generalizing in the first case a Theorem proved independently by F.-G. Timmesfeld and S. Smith. The paper is the first of a series dealing with linearization results…
We describe the qFunctions Mathematica package for $q$-series and partition theory applications. This package includes both experimental and symbolic tools. The experimental set of elements includes guessers for $q$-shift equations and…
An extension of the method and results of A. Schwarz for evaluating the partition function of a quadratic functional is presented. This enables the partition functions to be evaluated for a wide class of quadratic functionals of interest in…
In this paper, we characterize complementable operators and provide more precise expressions for the Schur complement of these operators using a single Douglas solution. We demonstrate the existence of subspaces where the given operator is…
The splitting of a $Q$-deformed boson, in the $Q\to q=e^{\frac{\QTR{rm}{2\pi i}}{\QTR{rm}{k}}}$ limit, is discussed. The equivalence between a $Q$-fermion and an ordinary one is established. The properties of the quantum (super)Virasoro…
Exploiting Virasoro constraints on the effective finite-volume partition function, we derive generalized Leutwyler-Smilga spectral sum rules of the Dirac operator to high order. By introducing $N_v$ fermion species of equal masses, we next…