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Home > Vol 17, No 2 (2003)

Momar Dieng , Tom Halverson² and Vahe Poladian³

²Department of Mathematics and Computer Science, Macalester College, Saint Paul, Minnesota 55105, USA

The q-rook monoid R _n( q) is a semisimple U _q \mathfrak g\mathfrak l( r) U_q {\mathfrak{g}}{\mathfrak{l}}(r) to compute a Frobenius formula, in the ring of symmetric functions, for the irreducible characters of R _n( q). We then derive a recursive Murnaghan-Nakayama rule for these characters, and we use Robinson-Schensted-Knuth insertion to derive a Roichman rule for these characters. We also define a class of standard elements on which it is sufficient to compute characters. The results for R _n( q) specialize when q = 1 to analogous results for R _n.

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