Conjugacy classes in the symplectic Renner monoid

Abstract

In this paper we study conjugacy classes of the symplectic Renner monoid R , and find the following results. Each element in 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.