A criterion on the semisimple Brauer algebras II

In [H. Rui, A criterion on the semisimple Brauer algebras, J. Combin. Theory Ser. A 111 (2005) 78–88], the first author gave an algorithm for determining the pairs (n,δ) such that the Brauer algebra Bn(δ) over a field F is semisimple. Such an algorithm involves a subset Z(n)⊂Z. In this note, we give an explicit description about Z(n). Using [H. Rui, A criterion on the semisimple Brauer algebras, J. Combin. Theory Ser. A 111 (2005) 78–88, 1.3] we verify Enyang's conjecture given in [J. Enyang, Specht modules and semisimplicity criteria for Brauer and Birman–Murakami–Wenzl algebras, preprint, 2005, 12.2].