Abstract
In this paper, we concern representations of symplectic rook monoids R. First, an algebraic description of R as a submonoid of a rook monoid is obtained. Second, we determine irreducible representations of R in terms of the irreducible representations of certain symmetric groups and those of the symplectic Weyl group W. We then give the character formula of R using the character of W and that of the symmetric groups. A practical algorithm is provided to make the formula user-friendly. At last we show that the Munn character table of R is a block upper triangular matrix.
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