Related papers: New solvable matrix models III
We give new product formulas for the number of standard Young tableaux of certain skew shapes and for the principal evaluation of the certain Schubert polynomials. These are proved by utilizing symmetries for evaluations of factorial Schur…
In this paper we introduce doubly symmetric functions, arising from the equivalence of particular linear combinations of Schur functions and hook Schur functions. We study algebraic and combinatorial aspects of doubly symmetric functions,…
We obtain a presentation of Schur algebras (and q-Schur algebras) by generators and relations which is compatible with the usual presentation of the enveloping algebra (quantized enveloping algebra) corresponding to the Lie algebra gl(n) of…
The soldering procedure has been for the first time generalized to the case of spin-3/2 fermionic theories. We have demonstrated that the fermionic part of the so called "New Topologically Massive Supergravity" theory, which is of third…
We present relations between Hirota-type bilinear operators, scalar products on spaces of symmetric functions and integrals defining matrix model partition functions. Using the fermionic Fock space representation, a proof of the expansion…
A systematic study of the discrete second order projective system is presented, complemented by the integrability analysis of the associated multilinear mapping. Moreover, we show how we can obtain third order integrable equations as the…
We introduce the concept of multiplication matrices for ideals of projective dimension zero. We discuss various applications and in particular, we give a new algorithm to compute the variety of an ideal of projective dimension zero.
We give combinatorial proofs that certain families of differences of products of Schur functions are monomial-positive. We show in addition that such monomial-positivity is to be expected of a large class of generating functions with…
Inspired by a recently proposed GUT model based on the trinification ($\mathrm{SU}(3)^3$) gauge group with a global family ($\mathrm{SU}(3)_F$) symmetry, we consider an effective low-energy three Higgs doublet model that may shed light on…
A nested Schur complement solver is proposed for iterative solution of linear systems arising in exponential and implicit time integration of the Maxwell equations with perfectly matched layer (PML) nonreflecting boundary conditions. These…
The double scaling limit of a new class of the multi-matrix models proposed in \cite{MMM91}, which possess the $W$-symmetry at the discrete level, is investigated in details. These models are demonstrated to fall into the same universality…
In this paper, using the theory of category, we generalize known properties of symmetric polynomials and functions and characterize the multi-indicial symmetric functions. Examples have been given on Schur functions.
Landen transformation, and more generally modular correspondences, can be seen to be exact symmetries of some integrable lattice models, like the square Ising model, or the Baxter model. They are solutions of remarkable Schwarzian equations…
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…
We define a new class of integrable vertex models associated to quantum groups at roots of unit
Aspects of three dimensional $\mathcal{N}=2$ gauge theories with monopole superpotentials and their dualities are investigated. The moduli spaces of a number of such theories are studied using Hilbert series. Moreover, we propose new…
We present a friendly introduction to the very detailed results in [9,10,11] and as an illustration we discuss here the issue of {\em linearization of products}. We find some interesting new phenomena.
We consider the simplest gauge theories given by one- and two- matrix integrals and concentrate on their stringy and geometric properties. We remind general integrable structure behind the matrix integrals and turn to the geometric…
We classify the module categories over the double (possibly twisted) of a finite group.
We continue the study of projective module wavelet frames corresponding to diagonal dilation matrices on $\mathbb R^n$ with integer entries, focusing on the construction of a projective multi-resolution analysis corresponding to dilations…