SYMMETRIZER FOR THE QUANTIZED WALLED BRAUER ALGEBRAS

摘要

Let s, r ∈ N and B_(s,r)~λ(q) be the quantized walled Brauer algebra. The quantized walled Brauer algebra admits two distinct one-dimensional representations. These are generated by central elements of B_(s,r)~λ(q) called the symmetrizer and the anti-symmetrizer of B_(s,r)~λ(q). We compute explicitly the coefficients of these two elements with respect to a diagrammatic basis of B_(s,r)~λ(q).