Geodesic
A Specht module analog for the rook monoid
The electronic journal of combinatorics, Tome 9 (2002)
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The wealth of beautiful combinatorics that arise in the representation theory of the symmetric group is well-known. In this paper, we analyze the representations of a related algebraic structure called the rook monoid from a combinatorial angle. In particular, we give a combinatorial construction of the irreducible representations of the rook monoid. Since the rook monoid contains the symmetric group, it is perhaps not surprising that the construction outlined in this paper is very similar to the classic combinatorial construction of the irreducible $S_n$-representations: namely, the Specht modules.
DOI : 10.37236/1619
Classification : 05E10, 20M30
Mots-clés : rook monoid, irreducible representations, Specht modules 
@article{10_37236_1619,
     author = {Cheryl Grood},
     title = {A {Specht} module analog for the rook monoid},
     journal = {The electronic journal of combinatorics},
     year = {2002},
     volume = {9},
     doi = {10.37236/1619},
     zbl = {0982.05107},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1619/}
}
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Cheryl Grood. A Specht module analog for the rook monoid. The electronic journal of combinatorics, Tome 9 (2002). doi: 10.37236/1619

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