On tensor categories of Lie Type EN, N≠9

Abstract

Let V be the minuscule representation of the Lie algebra g(E N) , N=6,7. We show that the centralizer of the action of the quantum group U q g(E N) on V ⊗ n is generated by the R-matrices and one additional element, appearing in the ( N−1)st tensor power; a similar description can be given for the classical limit. An analogous statement is true for a certain direct summand of V ⊗ n for U q g(E N) with N>5, N≠9 ; here V is the module whose highest weight is the fundamental weight labeled by the vertex furthest from the triple point of the graph E N . Moreover, we obtain a 2-parameter family of braid representations generalizing a q-version of the Brauer centralizer algebras.