Related papers: One-dimensional nil-DAHA and Whittaker functions
Let $\mathbb F$ denote a field, and fix a nonzero $q\in\mathbb F$ such that $q^4\not=1$. The universal Askey-Wilson algebra $\Delta_q$ is the associative $\mathbb F$-algebra defined by generators and relations in the following way. The…
We derive non-linear differential equations for correlation functions of U(1) twist fields in the two-dimensional massive Dirac theory. Primary U(1) twist fields correspond to exponential fields in the sine-Gordon model at the free-fermion…
We study $4$-dimensional $SU(N)\times U(1)$ gauge theories with a single massless Dirac fermion in the $2$-index symmetric/antisymmetric representations and show that they are endowed with a noninvertible $0$-form $\widetilde {\mathbb…
We consider a system of three commuting difference operators in three variables $x_{12},x_{13},x_{23}$ with two generic complex parameters $q,t$. This system and its eigenfunctions generalize the trigonometric $A_1$ Ruijsenaars-Schneider…
This paper studies rational functions $\mathfrak{J}_\alpha(q)$, which depend on a positive element $\alpha$ of the root lattice of a root system. These functions arise as Shapovalov pairings of Whittaker vectors in Verma modules of highest…
We provide a functional characterization of isometries between non-reversible Finsler manifolds, in the form of a generalization of the Myers-Nakai Theorem for Riemannian manifolds. We show that, since non-reversible Finsler manifolds are a…
Our objective is to usher and investigate the subclass$\widetilde{\mathcal{S^{*}_{\sum}}}^{\eta}_{q}(\mu,\lambda;\phi)$ of the function class $\sum$ of analytic and bi-univalent functions related with the symmetric $q$-derivative operator…
This thesis deals with a class of integrable field theories called models with twist function. The main examples of such models are integrable non-linear sigma models, such as the Principal Chiral Model, and their deformations. A first…
The first part of this work consists of a study of the ODE/IM correspondence for simply-laced affine Toda field theories. It is a first step towards a full generalisation of the results of Lukyanov and Zamolodchikov on $\hat{\mathfrak a}_1$…
The theory of quantum symmetric pairs is applied to $q$-special functions. Previous work shows the existence of a family $\chi$-spherical functions indexed by the integers for each Hermitian quantum symmetric pair. A distinguished family of…
The mode solutions of the Dirac equation on $N$-dimensional de Sitter space-time ($dS_{N}$) with $(N-1)$-sphere spatial sections are obtained by analytically continuing the spinor eigenfunctions of the Dirac operator on the $N$-sphere…
We present the fermionic representation for the q-deformed hypergeometric functions related to Schur polynomials considered by S.Milne \cite{Milne}. For $q=1$ these functions are also known as hypergeometric functions of matrix argument…
Zhedanov's algebra AW(3) is considered with explicit structure constants such that, in the basic representation, the first generator becomes the second order q-difference operator for the Askey-Wilson polynomials. It is proved that this…
In this document I develop a weight function theory of positive order basis function interpolants and smoothers. **In Chapter 1 the basis functions and data spaces are defined directly using weight functions. The data spaces are used to…
Ward-Takahashi identities are nonperturbative relations between correlation functions and arising from symmetries in quantum and statistical fields theories, as Noether currents conservation for classical theories. Since their historical…
A classical way to introduce tau functions for integrable hierarchies of solitonic equations is by means of the Sato-Segal-Wilson infinite-dimensional Grassmannian. Every point in the Grassmannian is naturally related to a Riemann-Hilbert…
The paper is an inquiry of the algebraic foundations of the theory of dispersionless integrable hierarchies, like the dispersionless KP and modified KP hierarchies and the universal Whitham's hierarchy of genus zero. It stands out for the…
In this paper we consider axisymmetric black holes in supergravity and address the general issue of defining a first order description for them. The natural setting where to formulate the problem is the De Donder-Weyl-Hamilton-Jacobi theory…
Let R be a 1-dimensional integral domain, let h (non-zero) be a prime element, and let \HA be the category of torsionless Hopf algebras over R. We call H in \HA a "quantized function algebra" (=QFA), resp. "quantized restricted universal…
Progress along the line of a previous article are reported. One main point is to include chiral operators with fractional quantum group spins (fourth or sixth of integers) which are needed to achieve modular invariance. We extend the study…