Related papers: Weyl denominator identity for the affine Lie super…
Weyl denominator identity for the affinization of a basic Lie superalgebra with a non-zero Killing form was formulated by Kac and Wakimoto and was proven by them in defect one case. In this paper we prove this identity.
Weyl denominator identity for finite-dimensional Lie superalgebras, conjectured by V.~Kac and M.~Wakimoto in 1994, is proven.
The study of denominator identities for Lie superalgebras was recently developed by M. Gorelik, V.G. Kac, P.Moseneder Frajria, I. Musson, P. Papi, M. Wakimoto and the author. In this paper we generalize these identities to the twisted…
In 1994, Kac and Wakimoto found the denominator identity for classical affine Lie superalgebras, generalizing that for affine Lie algebras. As an application, they obtained power series identities for some powers of $\triangle(q)$, where…
Character formulas for Lie superalgebras have been shown to have important applications to number theory and combinatorics. We prove the Kac-Wakimoto character formula for the general linear Lie superalgebra gl(m|n). This formula…
Weyl modules were originally defined for affine Lie algebras by Chari and Pressley in \cite{CP}. In this paper we extend the notion of Weyl modules for a Lie algebra $\mathfrak{g} \otimes A$, where $\mathfrak{g}$ is any Kac-Moody algebra…
In a paper by Su and Zhao, the Lie algebra $A[D]=A\otimes F[D]$ of Weyl type was defined and studied, where $A$ is a commutative associative algebra with an identity element over a field $F$ of arbitrary characteristic, and $F[D]$ is the…
We define a family of universal finite-dimensional highest weight modules for affine Lie algebras, we call these Weyl modules. We conjecture that these are the classical limits of the irreducible finite--dimensional representations of the…
We prove the conjecture of Frenkel, Kac and Wakimoto on the existence of two-sided BGG resolutions of G-integrable admissible representations of affine Kac-Moody algebras at fractional levels. As an application we establish the…
The theory of generalized Weyl algebras is used to study the $2\times 2$ reflection equation algebra $\mathcal{A}=\mathcal{A}_q(\operatorname{M}_2)$ in the case that $q$ is not a root of unity, where the $R$-matrix used to define…
We study Lie subalgebras $L$ of the vector fields $\mathrm{Vec}^{c}({\mathbb A}^{2})$ of affine 2-space ${\mathbb A}^{2}$ of constant divergence, and we classify those $L$ which are isomorphic to the Lie algebra $\mathfrak{aff}_{2}$ of the…
We prove a denominator identity for non-twisted affine Lie superalgebras with zero dual Coxeter number.
We define global and local Weyl modules for Lie superalgebras of the form $\mathfrak{g} \otimes A$, where $A$ is an associative commutative unital $\mathbb{C}$-algebra and $\mathfrak{g}$ is a basic Lie superalgebra or $\mathfrak{sl}(n,n)$,…
For a restricted Lie superalgebra g over an algebraically closed field of characteristic p > 2, we generalize the deformation method of Premet and Skryabin to obtain results on the p-power and 2-power divisibility of dimensions of…
We introduce and begin to study Lie theoretical analogs of symplectic reflection algebras for a finite cyclic group, which we call "cyclic double affine Lie algebra". We focus on type A : in the finite (resp. affine, double affine) case, we…
In a recent paper by Zhao and the author, the Lie algebras $A[D]=A\otimes F[D]$ of Weyl type were defined and studied, where $A$ is a commutative associative algebra with an identity element over a field $F$ of any characteristic, and…
We derive the fusion rules for a basic series of admissible representations of $\hat{sl}(3)$ at fractional level $3/p-3$. The formulae admit an interpretation in terms of the affine Weyl group introduced by Kac and Wakimoto. It replaces the…
We obtain Drinfeld second realization of the quantum affine superalgebras associated with the affine Lie superalgebra $D^{(1)}(2,1;x)$. Our results are analogous to those obtained by Beck for the quantum affine algebras. Beck's analysis…
This is a survey paper about affine Hecke algebras. We start from scratch and discuss some algebraic aspects of their representation theory, referring to the literature for proofs. We aim in particular at the classification of irreducible…
In this paper explicit decompositions are provided of the Weyl reflections in affine Lie algebras, in terms of fundamental Weyl reflections.