We introduce the notion of “local system of ZT -twisted vertex operators” on a Z2-graded vector space M , generalizing the notion of local system of vertex operators [Li]. First, we prove that any local system of ZT -twisted vertex operators on M has a vertex superalgebra structure with an automorphism σ of order T with M as a σ-twisted module. Then we prove that for a vertex (operator) superal...

We describe a Gauss decomposition for the Yangian Y (glm|n) of the general linear Lie superalgebra. This gives a connection between this Yangian and the Yangian of the classical Lie superalgebra Y (A(m− 1, n− 1)) (with m 6= n) defined and studied in papers by Stukopin, and suggests natural definitions for the Yangians Y (sln|n) and Y (A(n, n)). We also show that the coefficients of the quantum ...

A Gel’fand-Zetlin basis is introduced for the irreducible covariant tensor representations of the Lie superalgebra gl(m|n). Explicit expressions for the generators of the Lie superalgebra acting on this basis are determined. Furthermore, Clebsch-Gordan coefficients corresponding to the tensor product of any covariant tensor representation of gl(m|n) with the natural representation V ([1, 0, . ....

Solutions of the classical dynamical Yang-Baxter equation on a Lie superalgebra are called super dynamical r-matrices. A super dynamical r-matrix r satisfies the zero weight condition if [h⊗ 1 + 1⊗ h, r(λ)] = 0 for all h ∈ h, λ ∈ h∗. In this paper we explicitly quantize zero-weight super dynamical r-matrices with zero coupling constant for the Lie superalgebra gl(m,n). We also answer some quest...

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...