PARTIALLY HARMONIC TENSORS AND QUANTIZED SCHUR WEYL DUALITY

Let l, n epsilon N and g epsilon{(o)2l+1(C),(sp) 2l(C), (o)2l (C)}. Let V be the natural representation of the quantized enveloping algebra U-q (g) and B-n,B-q the specialized Birman-Murakami-Wenzl algebra with parameters depending on g (see (2) and Section 2 for their definitions). There is a Schur-Weyl duality between U-q(g) and B-n,B-q on V circle times(n). We prove that V circle times(n) can be decomposed into a direct sum of the subspaces of q-partially harmonic tensors of different valences and there is also a Schur Weyl duality between the Hecke algebra H-q(n) of type An_1 and U-q(g) on the subspaces of q-harmonic tensors. We construct explicitly a complete set of maximal vectors in V circle times(n) and identify some simple B-n,B-q -modules that they generate with the simple B-n,B-q-modules arising from Enyang's cellular basis of B-n,B-q.