Vust's Theorem and higher level Schur-Weyl duality for types B, C and D

Let G be a complex linear algebraic group, g = Lie(G) its Lie algebra and e is an element of g a nilpotent element. Vust's Theorem says that in case of C = GL(V), the algebra End(Ge) (V-circle times d), where G(e) subset of G is the stabilizer of e under the adjoint action, is generated by the image of the natural action of d-th symmetric group E-d and the linear maps {1(circle times(i-1)) circle times e circle times 1(circle times(d-i))vertical bar i = 1,..., d}. In this paper, we give an analogue of Vust's Theorem for G = O(V) and SP(V) when the nilpotent elements a satisfy that (G . e) over bar is normal. As an application, we study the higher Schur-Weyl duality in the sense of [4] for types B, C and D, which establishes a relationship between W-algebras and degenerate affine braid algebras. (C) 2017 Elsevier B.V. All rights reserved.