相关论文: Quantum matrix ball: differential and integral cal…
The q-monopole bundle introduced previously is extended to a general construction for quantum group bundles with non-universal differential calculi. We show that the theory applies to several other classes of bundles as well, including…
This paper is an enhanced version of a more than decade-older paper with a similar title. Many formulae involving both finite and infinite sums of digamma and polygamma functions up to quadratic order, few of which appear in standard…
In this paper, we tackle unresolved inquiries by Ferreira et al. \cite{bruno} in their recent publication, ``Functional Identity on Division Algebras". We delve into the intricate behavior of additive functions on matrix algebras over…
In Quantum Mechanics operators must be hermitian and, in a direct product space, symmetric. These properties are saved by Lie algebra operators but not by those of quantum algebras. A possible correspondence between observables and quantum…
The quantum even-dimensional balls are defined as the $C^*$-algebras generated by certain graphs. We exhibit a polynomial algebra for each even-dimensional quantum ball, and classify the irreducible representations of it.
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…
We introduce an algebra which describes the multiplication structure of a family of q-series containing a q-analogue of multiple zeta values. The double shuffle relations are formulated in our framework. They contain a q-analogue of…
The representation theory of the quantum group su$_q(2)$ is used to introduce $q$-analogues of the Wigner rotation matrices, spherical functions, and Legendre polynomials. The method amounts to an extension of variable separation from…
The aim of this paper is to evaluate in terms of q-special functions the objects (intertwining map, fusion matrix, exchange matrix) related to the quantum dynamical Yang-Baxter equation (QDYBE) for infinite dimensional representations…
A differential calculus on an associative algebra A is an algebraic analogue of the calculus of differential forms on a smooth manifold. It supplies A with a structure on which dynamics and field theory can be formulated to some extent in…
In this short note we extend a result of Jahangiri and Farahmand \cite{JM} concerning functions of bounded turning to a more general class of functions.
The aim of these notes is to provide a reasonably short and "hands-on" introduction to the differential calculus on associative algebras over a field of characteristic zero. Following a suggestion of Ginzburg's we call the resulting theory…
In this short survey article, we showcase a number of non-trivial geometric problems that have recently been resolved by marrying methods from functional calculus and real-variable harmonic analysis. We give a brief description of these…
In this paper, by the technique of inverse relations and comparing coefficients, we establish some generalized forms of Andrews' q-series identity and two new Bailey pairs and q-identities closely related to Andrews-Warnaar's sum identity…
From two q-summation formulas we deduce certain series expansion formulas involving the q-gamma function. With these formulas we can give q-analogues of series expansions for certain constants.
The aim of this paper is to present a simple way to generate proper monomial rational maps between generalized balls and via the relations between generalized balls and bounded symmetric domains of type I, we suggest new examples of proper…
In this paper we present equivalence results for several types of unbounded operator functions. A generalization of the concept equivalence after extension is introduced and used to prove equivalence and linearization for classes of…
In this article the quantized matrix algebras as in the title have been studied at a root of unity. A full classification of simple modules over such quantized matrix algebras of rank $2$ along with a class of finite dimensional…
In this thesis, the connection between recently introduced algebraic structures (tridiagonal algebra, $q$-Onsager algebra, generalized $q-$Onsager algebras), related representation theory (tridiagonal pair, Leonard pair, orthogonal…
We use derived Hall algebra of the category of nilpotent representations of Jordan quiver to reconstruct the theory of symmetric functions, focusing on Hall-Littlewood symmetric functions and various operators acting on them.