Vust's Theorem For Type B/C

Let G = GL(V1)× CL(V2),g=gl(V1)(?)gl(V2)its Lie algebra,and e = e1 + e2 ?g(e1?gl(V1),e2 ?gl(V2))a nilpotent element.Denote the centralizer of e in G by Ge:={g ?G|g-1eg=e}.This paper replaces the action of the Weyl group of type A on the tensor module V(?)d with that of the Weyl group of type B/C.We get Vust's theorem for type B/C:EndGe(V(?)d)is generated by the image of the action of the Weyl group of type B/C,linear maps 1(?)(i-1)(?)e1(?)1(?)(d-i),and 1(?)(i-1)(?)e2(?)1(?)(d-i)on the tensor module V(?)d.Based on this theorem,we establish a double centralizer property.