Conjugacy classes in the symplectic Renner monoid. (Q615866)

A symplectic Renner monoid is a non-Abelian submonoid of a rook monoid. The authors study conjugacy classes of the symplectic Renner monoid \(\mathcal R\), and find the following results. Each element in \(\mathcal R\) is a join of strictly disjoint cycles and strings. There is an explicit one-to-one correspondence between conjugacy classes and symplectic partitions. A formula for calculating the number of conjugacy classes is obtained. An explicit formula for computing the number of elements in each conjugacy class is given. A relationship between conjugacy classes and Munn conjugacy classes is described.