Irreducibility of fusion modules over twisted Yangians at generic point

Abstract

With any skew Young diagram one can associate a one parameter family of "elementary" modules over the Yangian $\Yg(\g\l_N)$. Consider the twisted Yangian $\Yg(\g_N)\subset \Yg(\g\l_N)$ associated with a classical matrix Lie algebra $\g_N\subset\g\l_N$. Regard the tensor product of elementary Yangian modules as a module over $\Yg(\g_N)$ by restriction. We prove its irreducibility for generic values of the parameters.