相关论文: A new aspect of representations of U_q(\hat{sl_2})…
The structure of the tensor product representation v_{\lambda_1}(x)\otimes V_{\lambda_2}(y) of U_q(\hat sl_2) is investigated at roots of unity. A polynomial identity is derived as an outcome. Also, new bases of v_{\lambda_1}(x)\otimes…
We present a proof of polynomial identities related to finite analogues of the branching functions of the coset $\widehat{sl(n)_1} \otimes \widehat{sl(n)_1} / \widehat{sl(n)_2}$.
A new approach to the theory of polynomial solutions of q - difference equations is proposed. The approach is based on the representation theory of simple Lie algebras and their q - deformations and is presented here for U_q(sl(n)). First a…
A general method of obtaining linear differential equations having polynomial solutions is proposed. The method is based on an equivalence of the spectral problem for an element of the universal enveloping algebra of some Lie algebra in the…
We formulate several polynomial identities. One side of these identities has a nice simple form. Whereas the other has a form of a polynomial whose coefficients contain binomial coefficients double factorials or (and) rising factorials. The…
We propose and prove a new polynomial identity that implies Schur's partition theorem. We give combinatorial interpretations of some of our expressions in the spirit of Kur\c{s}ung\"oz. We also present some related polynomial and $q$-series…
In this paper we give new identities involving q-Euler polynomials of higher order.
Given two combinatorial identities proved earlier, a new set of variations of these combinatorial identities is listed and proved with the integral representation method. Some identities from literature are shown to be special cases of…
In this note, we provide a conceptual explanation of a well-known polynomial identity used in algebraic number theory.
The Gelfand--Zetlin basis for representations of $U_q(sl(N))$ is improved to fit better the case when $q$ is a root of unity. The usual $q$-deformed representations, as well as the nilpotent, periodic (cyclic), semi-periodic (semi-cyclic)…
We describe a representation for $U_q(\widehat{sl(n)})$, when $q$ is not a root of unity, based on the fundamental representation of $sl(n)$. As $U_q(sl(n))$ has a Hopf algebra structure with a non-commutative co-product, we look for a…
In this paper, we fix a polynomial with complex coefficients and determine the eigenforms for SL2(Z) which can be expressed as the fixed polynomial evaluated at other eigenforms. In particular, we show that when one excludes trivial cases,…
Recently N.Jing discovered a certain combinatorial identity from validity of the Serre relations in some vertex representations of quantum Kac-Moody algebras. We generalize this identity, in particular, extending it from polynomials to…
Quantum groups at roots of unity have the property that their centre is enlarged. Polynomial equations relate the standard deformed Casimir operators and the new central elements. These relations are important from a physical point of view…
In this paper, we study some properties of associated sequaences in umbral calculus. From these properties, we derive new and interesting identities of several kinds of polynomials.
We show how to adapt the Gelfand-Zetlin basis for describing the atypical representation of ${\cal U}_{\displaystyle{q}}(sl(N))$ when $q$ is root of unity. The explicit construction of atypical representation is presented in details for…
The s ell_q(2) representations are realized in the space of polynomials for general and exceptional values of deformation parameter q and on finite set of theta-functions for cyclic representation corresponding to q^N = +/- 1, which are a…
A new $q$-analogue of Appell polynomial sequences and their generalizations are introduced and their main characterizations are proved. As consequences new $q$-analogue of Bernoulli and Euler polynomials and numbers is introduced, their…
The aim of this short note is to show how can be derived from the properties of fundamental interpolation polynomials some nice identities.
In this short note, we give a new sufficient condition for a linear map from a product of copies of a field to endomorphisms of a finite dimensional vector space over the same field to be an algebra homomorphism. We expect that this result…