相关论文: A PBW commutator lemma for U_q[gl(m|n)]
In this paper we study the tensor powers of the standard representation of the quantum super-algebra $U_q(sl(2|1)$, focusing on the rings of its algebra endomorphisms, called centraliser algebras and denoted by $LG_n$. Their dimensions were…
Let $W^c(A_n)$ be the set of fully commutative elements of the Coxeter group $W(A_n)$. Let $$ a_n(q)= \sum_{w \in W^c(A_n)} q^{l(w)} . $$ We compute $a_n(q)$.
We present a general method to deform the inhomogeneous algebras of the $B_n,C_n,D_n$ type, and find the corresponding bicovariant differential calculus. The method is based on a projection from $B_{n+1}, C_{n+1}, D_{n+1}$. For example we…
Quantum and q-deformed algebras find their application not only in mathematical physics and field theoretical context, but also in phenomenology of particle properties. We describe (i) the use of quantum algebras U_q(su_n) corresponding to…
The Fock space of $m+p$ bosonic and $n+q$ fermionic quantum oscillators forms a unitarizable module of the general linear superalgebra $gl_{m+p|n+q}$. Its tensor powers decompose into direct sums of infinite dimensional irreducible highest…
Pak and Panova recently proved that the $q$-binomial coefficient ${m+n \choose m}_q$ is a strictly unimodal polynomial in $q$ for $m,n \geq 8$, via the representation theory of the symmetric group. We give a direct combinatorial proof of…
We consider Lie superalgebras under constraints of Hamiltonian reduction, yielding finite $W$-superalgebras which provide candidates for quadratic spacetime superalgebras. These have an undeformed bosonic symmetry algebra (even generators)…
We prove that the Yangian associated to an untwisted symmetric affine Kac-Moody Lie algebra is isomorphic to the Drinfeld double of a shuffle algebra. The latter is constructed by the authors in arXiv:1407.7994 as an algebraic formalism of…
By using certain quantum differential operators, we construct a super representation for the quantum queer supergroup U_v(q_n). The underlying space of this representation is a deformed polynomial superalgebra in 2n^2 variables whose…
Using a super-realization of the Wigner-Heisenberg algebra a new realization of the q-deformed Wigner oscillator is implemented.
We classify extended Poincar\'e Lie super algebras and Lie algebras of any signature (p,q), that is Lie super algebras and Z_2-graded Lie algebras g = g_0 + g_1, where g_0 = so(V) + V is the (generalized) Poincar\'e Lie algebra of the…
In this paper we study an analogue of the classical Riemann-Hilbert problem stated for the classes of difference and $q$-difference systems. The Birkhoff's existence theorem was generalized in this paper.
An explicit construction of all finite-dimensional irreducible representations of the Lie superalgebra gl(1|n) in a Gel'fand-Zetlin basis is given. Particular attention is paid to the so-called star type I representations (``unitary…
We investigate non-commutative differential calculus on the supersymmetric version of quantum space where the non-commuting super-coordinates consist of bosonic as well as fermionic (Grassmann) coordinates. Multi-parametric quantum…
For the quantum algebra U_q(gl(n+1)) in its reduction on the subalgebra U_q(gl(n)) an explicit description of a Mickelsson-Zhelobenko reduction Z-algebra Z_q(gl(n+1),gl(n)) is given in terms of the generators and their defining relations.…
Using the curved bc-beta-gamma system (a tensor product of a Heisenberg and a Clifford vertex algebra) we introduce quantum analogy of Lichnerowicz differential. As follows we suggest new machinery for finding the Lichnerowicz-Poisson…
We obtain an interesting realization of the de Rham cohomological operators of differential geometry in terms of the noncommutative q-superoscillators for the supersymmetric quantum group GL_{qp} (1|1). In particular, we show that a unique…
In this paper the coherent state for $gl_q(n)$-covariant oscillators is constructed and is shown to satisfy the completeness relation. And the q-analogue of quantum mechanics in n dimensions is obtained by using $gl_q(n)$ oscillators.
By generalizing the Reshetikhin and Semenov-Tian-Shansky construction to supersymmetric cases, we obtain Drinfeld current realization for quantum affine superalgebra $U_q[gl(m|n)^{(1)}]$. We find a simple coproduct for the quantum current…
We present state sums for quantum link invariants arising from the representation theory of $U_q(\mathfrak{gl}_{N|M})$. We investigate the case of the $N$-th exterior power of the standard representation of $U_q(\mathfrak{gl}_{N|1})$ and…