On tensor spaces for Birman-Murakami-Wenzl algebras

Let l,nεN{double-struck}. Let sp2l be the symplectic Lie algebra over the complex number field C{double-struck}. Let V be the natural representation of the quantized enveloping algebra U{double-struck}_q(sp_2l) and B_n,q the specialized Birman-Murakami-Wenzl algebra with parameters -q^2l+1,q. In this paper, we construct a certain element in the annihilator of V^o×n in B_n,q, which comes from some one-dimensional two-sided ideal of Birman-Murakami-Wenzl algebra and is explicitly characterized (modulo the determination of some constants). We prove that the two-sided ideal generated by this element is indeed the whole annihilator of V^o×n in B_n,q and conjecture that the same is true over arbitrary ground fields and for any specialization of the parameter q. The conjecture is verified in the case when q is specialized to 1 (i.e., the Brauer algebra case) and the case when n=l+1.