Related papers: Factorial supersymmetric Schur functions and super…
We introduce interpolation analogues of Schur Q-functions - the multiparameter Schur Q-functions. We obtain for them several results: a combinatorial formula, generating functions for one-row and two-rows functions, vanishing and…
We establish the universality theorem for the first four symmetric power L-functions of automorphic forms and their associated Rankin-Selberg L-functions. This generalizes some results of Laurincikas & Matsumoto and Matsumoto respectively.
We construct differential algebras in which spaces of (one-dimensional) periodic ultradistributions are embedded. By proving a Schwartz impossibility type result, we show that our embeddings are optimal in the sense of being consistent with…
It is well known that if one integrates a Schur function indexed by a partition $\lambda$ over the symplectic (resp. orthogonal) group, the integral vanishes unless all parts of $\lambda$ have even multiplicity (resp. all parts of $\lambda$…
A ladder structure of operators is presented for the Jacobi polynomials, J_n^(a,b)(x), with parameters n, a and b integers, showing that they are related to the unitary irreducible representation of SU(2,2) with quadratic Casimir…
We study several quiver Chern-Simons-matter theories on the three-sphere, combining the matrix model formulation with a systematic use of Mordell's integral, computing partition functions and checking dualities. We also consider Wilson…
We consider a realization of supersymmetric quantum mechanics where supercharges are differential-difference operators with reflections. A supersymmetric system with an extended Scarf I potential is presented and analyzed. Its…
We make a systematic study of a new combinatorial construction called a dual equivalence graph. We axiomatize these graphs and prove that their generating functions are symmetric and Schur positive. This provides a universal method for…
A set of functions is introduced which generalizes the famous Schur polynomials and their connection to Grasmannian manifolds. These functions are shown to provide a new method of constructing solutions to the KP hierarchy of nonlinear…
Using the analytical expressions for the genuine eigenfunctions $\varphi_{\mu\nu}(z)$ and eigenvalues $E_{\mu,\nu}$, of open, bounded and quasi-bounded finite periodic systems, we derive the eigenfunctions space-inversion symmetry…
Similarity symmetries of the factorization chains for one-dimensional differential and finite-difference Schr\"odinger equations are discussed. Properties of the potentials defined by self-similar reductions of these chains are reviewed. In…
Consider the algebra Q<<x_1,x_2,...>> of formal power series in countably many noncommuting variables over the rationals. The subalgebra Pi(x_1,x_2,...) of symmetric functions in noncommuting variables consists of all elements invariant…
In this note we develop a systematic combinatorial definition for constructed earlier supersymmetric polynomial families. These polynomial families generalize canonical Schur, Jack and Macdonald families so that the new polynomials depend…
In this paper, we extend the results of Grantcharov and Robitaille in 2021 on mixed tensor products and Capelli determinants to the superalgebra setting. Specifically, we construct a family of superalgebra homomorphisms $\varphi_R :…
We introduce a general method for constructing modules for $0$-Hecke algebras and supermodules for $0$-Hecke-Clifford algebras from diagrams of boxes in the plane, and give formulas for the images of these modules in the algebras of…
In an earlier work extensions of supersymmetry and super Lie algebras were constructed consistently starting from any representation $\D$ of any Lie algebra $\g$. Here it is shown how infinite dimensional Lie algebras appear naturally…
In this article, we study the notion of central extension of Leibniz $n$-algebras relative to $n$-Lie algebras to study properties of Schur $\mathsf{Lie}$-multiplier and $\mathsf{Lie}$-covers on Leibniz $n$-algebras. We provide a…
This is an overview of recent results on the use of 2D Toda $\tau$-functions as generating functions for multiparametric families of weighted Hurwitz numbers. The Bose-Fermi equivalence composed with the characteristic map provides an…
We introduce an extended Kepler-Coulomb quantum model in spherical coordinates. The Schr\"{o}dinger equation of this Hamiltonian is solved in these coordinates and it is shown that the wave functions of the system can be expressed in terms…
In this paper a new supersymmetric extension of conformal mechanics is put forward. The beauty of this extension is that all variables have a clear geometrical meaning and the super-Hamiltonian turns out to be the Lie-derivative of the…