We introduce a new family of central elements the Yangian queer Lie superalgebra [Formula: see text].

We derive a new expression for the supersymmetric Schur polynomials sλ(x/y). The origin of this formula goes back to representation theory of the Lie superalgebra gl(m|n) and gives rise to a determinantal formula for sλ(x/y). In the second part, we use this determinantal formula to derive new expressions for the dimension and superdimension of covariant representations Vλ of the Lie superalgebr...

We study stabilization of finite-dimensional representations the periplectic Lie superalgebras $\mathfrak{p}(n)$ as $n \to \infty$. The paper gives a construction tensor category $Rep(\underline{P})$, possessing nice universal properties among categories over $\mathtt{sVect}$ complex vector superspaces. First, it is abelian envelope Deligne corresponding to superalgebra, in sense arXiv:1511...

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...