Related papers: Determinantal formulas for Sklyanin-Whittaker inte…
For a real affine hyperplane arrangement, we define an integer intersection matrix with a natural $q$-deformation related to the intersections of bounded chambers of the arrangement. By connecting the integer matrix to a bilinear form of…
In this note we outline the history of q-deformations; indicate their physical shortcomings; suggest their apparent resolution via an invariant formulation based on a new mathematics of genotopic type; and point out their expected physical…
We prove a duality formula between two elliptic determinants. We present a proof which is a variant of the Izergin-Korepin method which is a method originally introduced to analyze and compute partition functions of integrable lattice…
We survey various classical results on invariants of polynomials, or equivalently, of binary forms, focussing on explicit calculations for invariants of polynomials of degrees 2, 3, 4.
In this paper, we clarified the relationship between continued fractions, determinants, and identities, making it easier to apply these methods systematically in other settings. In particular, we studied finite continued fractions from the…
We consider linear and quadratic integrals of motion for general variable quadratic Hamiltonians. Fundamental relations between the eigenvalue problem for linear dynamical invariants and solutions of the corresponding Cauchy initial value…
In this paper, the solution of the multi-order differential equations, by using Mellin Transform, is proposed. It is shown that the problem related to the shift of the real part of the argument of the transformed function, arising when the…
Discrete series Whittaker functions on $Spin(2n, 2)$ are studied. The dimensions of the space of both algebraic and continuous Whittaker models are explicitly determined. They are described by a sum of dimensions of irreducible…
We study the differential smoothness of Sklyanin algebras in three and four variables. We show that all non-degenerate three-dimensional cases are differentially smooth, while none of the four-dimensional Sklyanin algebras admit a connected…
It is known that determinantal point processes have an intimate relation to operator algebras. In the paper, we extend this relationship to encompass dynamical aspects. Especially, we delve into two types of determinantal point processes.…
We express the defining relations of the $q$-deformed Minkowski space algebra as well as that of the corresponding derivatives and differentials in the form of reflection equations. This formulation encompasses the covariance properties…
We introduce a one parameter deformation of Zwegers' multivariable $\mu$-function by applying iterations of the $q$-Borel summation method, which is also a multivariate analogue of the generalized $\mu$-function introduced by the authors.…
Counting integral binary quadratic forms with certain restrictions is a classical problem. In this paper, we count binary quadratic forms of fixed discriminant given restrictions on the size of their coefficients. We accomplish this by…
We express covariance of the Batalin-Vilkovisky formalism in classical mechanics by means of the Maurer-Cartan equation in a curved Lie superalgebra, defined using the formal variational calculus and Sullivan's Thom-Whitney construction. We…
We construct planar semimartingales that include the Walsh Brownian motion as a special case, and derive Harrison-Shepp-type equations and a change-of-variable formula in the spirit of Freidlin-Sheu for these so-called "Walsh…
Using determinant functor, we describe a natural transformation from local Hilbert functor to K-theoretic cycle groups of codimension one, which were variants of Balmer's tensor triangular Chow groups. This enables us to answers a question…
We describe a unifying framework for the systematic construction of integrable deformations of integrable $\sigma$-models within the Hamiltonian formalism. It applies equally to both the `Yang-Baxter' type as well as `gauged WZW' type…
We discuss several aspects of Mellin transform, including distributional Mellin transform and inversion of multiple Mellin-Barnes integrals in $\mathbb{C}^n$ and its connection to residue expansion or evaluation of Laplace integrals. These…
We establish Plemelj-Smithies formulas for determinants in different algebras of operators. In particular we define a Poincar\'e type determinant for operators on the torus $\Tn$ and deduce formulas for determinants of periodic…
We obtain a complete description of the integer group determinants for $Q_{16},$ the dicyclic or generalized quaternion group of order 16.