Geodesic
Character formulas for $q$-rook monoid algebras
Journal of Algebraic Combinatorics, Tome 17 (2003) no. 2, pp. 99-123.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: The $q$-rook monoid $R _{n}( q)$ is a semisimple $U _{ q} \mathfrak g\mathfrak l( r)$ U_q mathfrakgmathfrakl$(r)$ 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 $R _{n}$.
Keywords: rook monoid, character, Hecke algebra, symmetric functions 
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     title = {Character formulas for $q$-rook monoid algebras},
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Dieng, Momar; Halverson, Tom; Poladian, Vahe. Character formulas for $q$-rook monoid algebras. Journal of Algebraic Combinatorics, Tome 17 (2003) no. 2, pp. 99-123. http://geodesic.mathdoc.fr/item/JAC_2003__17_2_a5/