Related papers: Quantum Reduction for Affine Superalgebras
We define a reduction covariant for the representations a la Vinberg associated to stably graded Lie algebras. We then give an analogue of the LLL algorithm for the odd split special orthogonal group and show how this can be combined with…
We describe a generalization of Drinfeld's description of the center of a quantum group to the case of quantum affine algebras. We use the obtained central elements to construct the affine analogue of Macdonald's difference operators.
Some basic ideas of the Refined Algebraic Quantization scheme are outlined at an intuitive level, using a class of simple models with a single wave equation as quantum constraint. In addition, hints are given how the scheme is applied to…
Maximal parabolic subalgebras of untwisted affine Kac-Moody algebras were studied in the context of Borel-de Siebenthal theory in [13], where they were realized as certain equivariant map algebras with a non-free abelian group action. In…
Quantum multiparameter deformation of real Clifford algebras is proposed. The corresponding irreducible representations are found.
Generators and relations are given for the subalgebra of cocommutative elements in the quantized coordinate rings of the classical groups, where the deformation parameter q is transcendental. This is a ring theoretic formulation of the well…
We prove that the specialization to q=1 of a Kirillov-Reshetikhin module for an untwisted quantum affine algebra of classical type is projective in a suitable category. This yields a uniform character formula for the Kirillov-Reshetikhin…
Assuming that there exist operators which form an irreducible representation of the q-superoscillator algebra, it is proved that any two such representations are equivalent, related by a uniquely determined superunitary transformation. This…
Associated to quantum affine general linear Lie superalgebras are two families of short exact sequences of representations whose first and third terms are irreducible: the Baxter TQ relations involving infinite-dimensional representations;…
Affine W-algebras are a somewhat complicated family of (topological) associative algebras associated with a semisimple Lie algebra, quantizing functions on the algebraic loop space of Kostant's slice. They have attracted a great deal of…
Quantum affine reflection algebras are coideal subalgebras of quantum affine algebras that lead to trigonometric reflection matrices (solutions of the boundary Yang-Baxter equation). In this paper we use the quantum affine reflection…
With this paper we hope to contribute to the theory of quantales and quantale-like structures. It considers the notion of $Q$-sup-algebra and shows a representation theorem for such structures generalizing the well-known representation…
The main purpose of this paper is to define representations and a cohomology of color Hom-Lie algebras and to study some key constructions and properties. We describe Hartwig-Larsson-Silvestrov Theorem in the case of $\Gamma$-graded…
In this paper we introduce new affine algebraic varieties whose points correspond to associative algebras. We show that the algebras within a variety share many important homological properties. In particular, any two algebras in the same…
A simple method is proposed for deforming $A_\infty$-algebras by means of the resolution technique. The method is then applied to the associative algebras of polynomial functions on quantum superspaces. Specifically, by introducing suitable…
We extend a conjugacy Theorem of Cartan subalgebras, originally established for symmetrizable Kac-Moody algebras, to the broader context of affine Kac-Moody superalgebras. Along the way, we obtain several results that deepen our…
The quantum affine $\CU_q (\hat{sl(2)}) $ symmetry is studied when $q^2$ is an even root of unity. The structure of this algebra allows a natural generalization of N=2 supersymmetry algebra. In particular it is found that the momentum…
Let $\Gamma$ be a finite subgroup of $\SL_2(\C)$. We consider $\Gamma$-fixed point sets in Hilbert schemes of points on the affine plane $\C^2$. The direct sum of homology groups of components has a structure of a representation of the…
We use category theory to propose a unified approach to the Schur-Weyl dualities involving the general linear Lie algebras, their polynomial extensions and associated quantum deformations. We define multiplicative sequences of algebras…
In this paper we use the Etingof-Kazhdan quantization of Lie bi-superalgebras to investigate some interesting questions related to Drinfeld-Jimbo type superalgebra associated to a Lie superalgebra of classical type. It has been shown that…