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 B n ( 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 Enyangʹs conjecture given in [J. Enyang, Specht modules and semisimplicity criteria for Brauer and Birman–Murakami–Wenzl algebras, preprint, 2005, 12.2].