Related papers: The Thom Class and Localization of SUSY QM Generat…
We apply the generalized formalism and the techniques of the supersymmetric (susy) quantum mechanics to the cases where the superpotential is generated/defined by higher excited eigenstates (Robnik 1997, paper I). The generalization is…
Different ways to incorporate two-dimensional systems, which are not amenable to separation of variables, into the framework of Supersymmetrical Quantum Mechanics (SUSY QM) are analyzed. In particular, the direct generalization of…
The familiar generating functionals in quantum field theory fail to be true measures and, so they make the sense only in the framework of the perturbation theory. In our approach, generating functionals are defined strictly as the Fourier…
We extend the standard intertwining relations used in Supersymmetrical (SUSY) Quantum Mechanics which involve real superpotentials to complex superpotentials. This allows to deal with a large class of non-hermitean Hamiltonians and to study…
We describe generating functions for several important families of classical symmetric functions and shifted Schur functions. The approach is originated from vertex operator realization of symmetric functions and offers a unified method to…
In [arXiv:1912.02063], we constructed 3-dimensional Topological Quantum Field Theories (TQFTs) using not necessarily semisimple modular categories. Here, we study projective representations of mapping class groups of surfaces defined by…
It is observed that the conjugacy growth series of the infinite finitary symmetric group with respect to the generating set of transpositions is the generating series of the partition function. Other conjugacy growth series are computed,…
This is the second paper in a series of papers aimed at providing a geometric construction of modular functors and topological quantum field theories from conformal field theory building on the constructions in [TUY] and [KNTY]. We give a…
Quantum theta functions were introduced by the author in [Ma1]. They are certain elements in the function rings of quantum tori. By definition, they satisfy a version of the classical functional equations involving shifts by the…
The connection between the generating functions of various sets of tableaux and the appropriate families of quasisymmetric functions is a significant tool to give a direct analytical proof of some advanced bijective results and provide new…
I review the appearence of integrable structures in the formulation of exact nonperturbative solutions to $4d$ supersymmetric quantum gauge theories. Various examples of ${\cal N}\geq 2$ SUSY Yang-Mills nonperturbative solutions are…
We show that in many cases nontrivial and complicated supersymmetric quantum mechanical (SQM) models can be obtained from the simple model describing free dynamics in flat complex space by two operations: (i) Hamiltonian reduction and (ii)…
We solve general 1-matrix models without taking the double scaling limit. A method of computing generating functions is presented. We calculate the generating functions for a simple and double torus. Our method is also applicable to more…
We derive generating functions for the ranks of pre-modular categories associated to quantum groups at roots of unity.
We compute the generating function for the characters of the irreducible representations of SU(n) whose associated Young diagrams have only two rows with the same number of boxes. The result is a rational determinantal expression in which…
For an integer $M\geq 2$ and a finite group $G$, an element $\alpha\in G$ is called an $M$-th power if it satisfies $A^M=\alpha$ for some $A\in G$. In this article, we will deal with the case when $G$ is finite symplectic or orthogonal…
We study generating functions of ordinary and plane partitions coloured by the action of a finite subgroup of the corresponding special linear group. After reviewing known results for the case of ordinary partitions, we formulate a…
In [5, 6] it has been proved that the ring of quasisymmetric functions over the integers is free polynomial, see also [4]. This is a matter that has been of great interest since 1972; for instance because of the role this statement plays in…
The present paper is the first installment where, extending our previous work in pure Yang-Mills (YM) theory, we compute the generating functional of correlators of collinear twist-$2$ operators that enter the components of balanced…
Extension procedure for supermanifold ${\cal M}_{cl}$ of superfields ${\cal A}^{\imath}(\theta)$, ghost number construction are considered. Classical and $\hbar$-deformed generating (master) equations, existence theorems for their solutions…