Related papers: On vertex operator realizations of Jack functions
Let V be a simple vertex operator algebra and G a finite automorphism group. Then there is a natural right G-action on the set of all inequivalent irreducible V-modules. Let S be a finite set of inequivalent irreducible V-modules which is…
This is a continuation of our work to understand vertex operator algebras using the geometric properties of varieties attached to vertex operator algebras. For a class of vertex operator algebras including affine vertex operator algebras…
We introduce FA-matrices for computing ranks of vector bundles of coinvariants and conformal blocks associated with modules over vertex operator algebras on the moduli space of stable pointed curves, unifying the notions of fusion and…
We study connections between closure operators on an algebra $(A,\Om)$ and congruences on the extended power algebra defined on the same algebra. We use these connections to give an alternative description of the lattice of all subvarieties…
We study several fundamental operators in harmonic analysis related to Jacobi expansions, including Riesz transforms, imaginary powers of the Jacobi operator, the Jacobi-Poisson semigroup maximal operator and Littlewood-Paley-Stein square…
We examine the question of when, and how, the norm of a vector functional on an operator algebra can be controlled by the invariant subspace lattice of the algebra. We introduce a related operator algebraic property, and show that it is…
A family of vertex operators that generalizes those given by Jing for the Hall-Littlewood symmetric functions is presented. These operators produce symmetric functions related to the Poincare polynomials referred to as generalized Kostka…
Hecke symmetries generalize the usual tensor symmetry of vector spaces $v\otimes w\arrow w\otimes v$ as well as the symmetry of vector superspaces. To a Hecke symmetry $R$ there associates a quadratic algebra which can be interpreted as the…
We present a free boson realization of the vertex operators and their duals for the solvable SOS lattice model of $A^{(1)}_{n-1}$ type. We discuss a possible connection to the calculation of the correlation functions.
In this paper, we introduce the concept of operator geometrically convex functions for positive linear operators and prove some Hermite-Hadamard type inequalities for these functions. As applications, we obtain trace inequalities for…
We develop a functional calculus on Archimedean vector lattices for semicontinuous positively homogeneous real-valued functions defined on $\R^n$ which are bounded on the unit sphere. It is further shown that this semicontinuous Archimedean…
We introduce the notion of regular operator mappings of several variables generalising the notion of spectral function. This setting is convenient for studying maps more general than what can be obtained from the functional calculus, and it…
Heckman and Opdam introduced a non-symmetric analogue of Jack polynomials using Cherednik operators. In this paper, we derive a simple recursion formula for these polynomials and formulas relating the symmetric Jack polynomials with the…
In this paper, we introduce operator geodesically convex and operator convex-log functions and characterize some properties of them. Then apply these classes of functions to present several operator Azc\'{e}l and Minkowski type inequalities…
We construct a generalization of the theory of symmetric functions involving functions of commuting and anticommuting (Grassmannian) variables. These new functions, called symmetric functions in superspace, are invariant under the diagonal…
The irreducible modules of the 2-cycle permutation orbifold models of lattice vertex operator algebras of rank 1 are classified, the quantum dimensions of irreducible modules and the fusion rules are determined.
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…
We introduce a generalization of symmetric functions and apply the resulting theory to compute the class in the Grothendieck ring of varieties of the space of geometrically irreducible hypersurfaces of a fixed degree in projective space.
The Heisenberg Oscillator Algebra admits irreducible representations both on the ring $B$ of polynomials in infinitely many indeterminates (the {\em bosonic representation}) and on a graded-by-{\em charge} vector space, the {\em…
In this article we determine the coefficient bounds for functions in certain subclasses of analytic functions defined by subordination which are related to the well-known classes of starlike and convex functions. The main results deal with…