Related papers: Jack vertex operators and realization of Jack func…
This paper investigates the transformation of determinants of pairs of Fredholm operators with trace class commutators. We study the extent to which the functional calculus commutes, modulo operator ideals, with projections in a finitely…
The Jack symmetric polynomials $P_\lambda^{(\alpha)}$ form a class of symmetric polynomials which are indexed by a partition $\lambda$ and depend rationally on a parameter $\alpha$. They reduced to the Schur polynomials when $\alpha=1$, and…
Vector-valued Jack polynomials associated to the symmetric group ${\mathfrak S}_N$ are polynomials with multiplicities in an irreducible module of ${\mathfrak S}_N$ and which are simultaneous eigenfunctions of the Cherednik-Dunkl operators…
Using the vertex operator representations for symplectic and orthogonal Schur functions, we define two families of symmetric functions and show thatthey are the skew symplectic and skew orthogonal Schur polynomials defined implicitly by…
We define cylindric generalisations of skew Macdonald functions when one of their parameters is set to zero. We define these functions as weighted sums over cylindric skew tableaux: fixing two integers n>2 and k>0 we shift an ordinary skew…
Introduced by Goulden and Jackson in their 1996 paper, the matchings-Jack conjecture and the hypermap-Jack conjecture (also known as the $b$-conjecture) are two major open questions relating Jack symmetric functions, the representation…
The Bernstein operator $\mathbf{B}_n$ acts on a Schur function $S_\lambda$ by appending a part to the index, i.e., $\mathbf{B}_n S_\lambda=S_{(n,\lambda)}$. This provides a method of constructing the vertex operator representation of Schur…
Some fixed point results are given for a class of functional contractions acting on (reflexive) triangular symmetric spaces. Technical connections with the corresponding theories over (standard) metric and partial metric spaces are also…
We study the orthogonal polynomials associated with the equilibrium measure, in logarithmic potential theory, living on the attractor of an Iterated Function System. We construct sequences of discrete measures, that converge weakly to the…
In this paper we improve results related to Normalized Jensen Functional for convex functions and Uniformly Convex Functions.
In the intersection of the theories of nonsymmetric Jack polynomials in $N$ variables and representations of the symmetric groups $\mathcal{S}_{N}$ one finds the singular polynomials. For certain values of the parameter $\kappa$ there are…
We first derive the transverse Ward-Takahashi identities (WTI) of 3-dimensional quantum electrodynamics (QED$_3$) by means of the canonical quantization method and the path integration method, and then prove for the first time that QED$_3$…
We generalize the tensor product theory for modules for a vertex operator algebra previously developed in a series of papers by the first two authors to suitable module categories for a ''conformal vertex algebra'' or even more generally,…
The principal results of this paper consist of an intrinsic definition of the Evans function in terms of newly introduced generalized matrix-valued Jost solutions for general first-order matrix-valued differential equations on the real…
The spectral decomposition for an explicit second-order differential operator $T$ is determined. The spectrum consists of a continuous part with multiplicity two, a continuous part with multiplicity one, and a finite discrete part with…
We define Donaldson-Thomas invariants of Calabi-Yau orbifolds and we develop a topological vertex formalism for computing them. The basic combinatorial object is the orbifold vertex, a generating function for the number of 3D partitions…
Given an operator L acting on a function space, the J-matrix method consists of finding a sequence y_n of functions such that the operator L acts tridiagonally on y_n with respect to n. Once such a tridiagonalization is obtained, a number…
We construct the generalized $\beta$ and $(q,t)$-deformed partition functions through $W$ representations, where the expansions are respectively with respect to the generalized Jack and Macdonald polynomials labeled by $N$-tuple of Young…
The fractional level models are (logarithmic) conformal field theories associated with affine Kac-Moody (super)algebras at certain levels $k \in \mathbb{Q}$. They are particularly noteworthy because of several longstanding difficulties that…
We consider Jack measures on partitions with homogeneous defining specializations. For each of the six distinct classes of measures obtained this way we prove a global law of large numbers with an explicit limiting particle density. We also…