-superalgebras as truncations of super-Yangians

Abstract

We show that some finite W-superalgebras based on gl(M |N ) are truncation of the super-Yangian Y (gl(M |N )). In the same way, we prove that finite W-superalgebras based on osp(M |2n) are truncation of the twisted super-Yangians Y (gl(M |2n)) + . Using this homomorphism, we present these W-superalgebras in an R-matrix formalism, and we classify their finite-dimensional irreducible representations.math.QA/0209339

Cohomological Hall Algebras, Vertex Algebras and Instantons

“…Recall the following correspondence from (12), which is used to define the action of H (Q3,W3) on V r1,r2,r3 , where n = n 1 + n 2 :…”

“…[88] conjectured appearance of modules induced from generic Gelfand-Tsetlin modules of [27] and various irregular modules of [41,43]. 12 For simplicity, we again decouple W 1 as in the Virasoro case above.…”

Finite W-Superalgebras and Truncated Super Yangians

“…When σ = 0, the two-sided ideal is generated by {t (r) i,j | 1 ≤ i, j ≤ m + n, r > ℓ}. In this special case, the quotient is exactly the truncated super Yangian in [BR,Pe2], which is a super analogy of Yangian of level ℓ due to Cherednik [C1, C2]. It should be clear from the context that we are dealing with Y µ (σ) or the quotient Y ℓ µ (σ) and hence, by abusing notation, we will use the same symbols D b,a;i,j to denote the elements in Y µ (σ) and their images in the quotient Y ℓ µ (σ).…”

On boundary superalgebras

“…The twisted super Yangian defined by [22,23,24] (for more details on the physical meaning of reflection algebra and twisted Yangian see [25,4]):…”