Related papers: $U_q^+(B_2)$ and its representations
We give unified modular proofs to all of Gosper's identities on the $q$-constant $\Pi_q$. We also confirm Gosper's observation that for any distinct positive integers $n_1,\cdots,n_m$ with $m\geq 3$, $\Pi_{q^{n_1}}$, $\cdots$,…
We give a $q$-analogue of some binomial coefficient identities of Y. Sun [Electron. J. Combin. 17 (2010), #N20] as follows: {align*} \sum_{k=0}^{\lfloor n/2\rfloor}{m+k\brack k}_{q^2}{m+1\brack n-2k}_{q} q^{n-2k\choose 2} &={m+n\brack…
Pseudo-BCI-algebras generalize both BCI-algebras and pseudo-BCK-algebras, which are a non-commutative generalization of BCK-algebras. In this paper, following [J.G. Raftery and C.J. van Alten, Residuation in commutative ordered monoids with…
Polynomial and spline quasi-interpolants (QIs) are practical and effective approximation operators. Among their remarkable properties, let us cite for example: good shape properties, easy computation and evaluation (no linear system to…
We describe the underlying U_q(g)--module structure of representations of quantum affine algebras.
The complex affine quadric $Q^{m}=\{z\in {\Bbb C}^{m+1}\mid z_{1}^{2}+...+z_{m+1}^{2}=1\}$ deforms by retraction onto $S^{m}$; this allows us to identify $[Q^{k},Q^{n}]$ and $[S^{k},S^{n}]=\pi_{k}(S^{n})$. Thus one will say that an element…
We study asymptotic behaviour of graded codimensions of Lie superalgebra $b(2)$. We prove that graded PI-exponent exists and is equal to $3+2\sqrt 3$.
The $q$-calculus for generic $q$ is developed and related to the deformed oscillator of parameter $q^{1/2}$. By passing with care to the limit in which $q$ is a root of unity, one uncovers the full algebraic structure of ${{\cal…
It is shown that when q is a primitive root of unity of order not equal to 2 mod 4, A(SL_q(2)) is a free module of finite rank over the coordinate ring of the classical group SL(2). An explicit set of generators is provided.
Let $UT_2$ be the algebra of $2\times 2$ upper triangular matrices over a field $F$ of characteristic zero. Here we study the generalized polynomial identities of $UT_2$, i.e., identical relations holding for $UT_2$ regarded as…
A method to construct in explicit form the generators of the simple roots of an arbitrary finite-dimensional representation of a quantum or standard semisimple algebra is found. The method is based on general results from the global theory…
For any open, connected and bounded set $\Omega \subseteq \mathbb C^m$, let $\mathcal A$ be a natural function algebra consisting of functions holomorphic on $\Omega$. Let $\mathcal M$ be a Hilbert module over the algebra $\mathcal A$ and…
In this paper we study the representation theory of filtered algebras with commutative associated graded whose spectrum has finitely many symplectic leaves. Examples are provided by the algebras of global sections of quantizations of…
A standard bicovariant differential calculus on a quantum matrix space ${\tt Mat}(m,n)_q$ is considered. The principal result of this work is in observing that the $U_q\frak{s}(\frak{gl}_m\times \frak{gl}_n))_q$ is in fact a…
Let $q$ be a positive integer. In our recent paper, we proved that the cardinality of the complement of an integral arrangement, after the modulo $q$ reduction, is a quasi-polynomial of $q$, which we call the characteristic…
We prove polynomial identities for the N=1 superconformal model SM(2,4\nu) which generalize and extend the known Fermi/Bose character identities. Our proof uses the q-trinomial coefficients of Andrews and Baxter on the bosonic side and a…
We compute the PI-exponent of the matrix ring with coefficients in an associative algebra. As a consequence, we prove the following. Let $\mathcal{R}$ be a PI-algebra with a positive PI-exponent. If $M_n(\mathcal{R})$ and $M_m(\mathcal{R})$…
In this paper, we study some symmetric identities of q-Euler numbers and polynomials. From these properties, we derive several identities of q-Euler numbers and polynomials.
In this paper, we investigate some properties of q-Bernoulli polynomi- als arising from q-umbral calculus. Finally, we derive some interesting identities of q-Bernoulli polynomials from our investigation.
We prove a bijection between finite-dimensional irreducible modules for an arbitrary quantum affine algebra $U_q(g)$ and finite-dimensional irreducible modules for its Borel subalgebra $U_q(g)^{\geq 0}$.