We study representations of the quantum affine superalgebra associated with a general linear Lie superalgebra. In the spirit of Hernandez–Jimbo, we construct inductive systems of Kirillov–Reshetikhin modules based on a cyclicity result that we established previously on tensor products of these modules, and realize their inductive limits as modules over its Borel subalgebra, the so-called q-Yang...

We prove denominator identities for the periplectic Lie superalgebra p ( n ) , thereby completing problem of finding all simple classical finite-dimensional superalgebras.

We define a notion of ghost centre of a Lie superalgebra g = g0 ⊕ g1 which is a sum of invariants with respect to the usual adjoint action (centre) and invariants with respect to a twisted adjoint action (“anticentre”). We calculate the anticentre in the case when the top external degree of g1 is a trivial g0-module. We describe the Harish-Chandra projection of the ghost centre for basic classi...

Abstract. An explicit construction of all finite-dimensional irreducible representations of classical Lie algebras is a solved problem and a Gelfand-Zetlin type basis is known. However the latter lacks the orthogonality property or does not consist of weight vectors for so(n) and sp(2n). In case of Lie superalgebras all finite-dimensional irreducible representations are constructed explicitly o...

Let e be an arbitrary even nilpotent element in the general linear Lie superalgebra glM|N and let We associated finite W-superalgebra. Ym|n super Yangian to glm|n. A subalgebra of Ym|n, called shifted denoted by Ym|n(σ), is defined studied. Moreover, explicit isomorphism between a quotient Ym|n(σ) established.

Let L be a finitely generated free color Lie superalgebra. We obtain new almost primitive and test elements of L. AMS Subject Classification: 17B01, 17B40

We describe the centre of a simple Lie superalgebra of type P (n). The description is based on the notion of anticentre.