Geodesic
Permutation resolutions for Specht modules.
Journal of Algebraic Combinatorics, Tome 34 (2011) no. 1, pp. 141-162.

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

Summary: For every composition $\lambda $ of a positive integer $r$, we construct a finite chain complex whose terms are direct sums of permutation modules $M ^{ \mu }$ for the symmetric group $\mathfrak S _{ r}$ mathfrakS_r with Young subgroup stabilizers $\mathfrak S _{ m}$ mathfrakS_mu. The construction is combinatorial and can be carried out over every commutative base ring $k$. We conjecture that for every partition $\lambda $ the chain complex has homology concentrated in one degree (at the end of the complex) and that it is isomorphic to the dual of the Specht module $S ^{ \lambda }$. We prove the exactness in special cases.
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Keywords: keywords symmetric group, permutation module, Specht module, resolution 
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     title = {Permutation resolutions for {Specht} modules.},
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     pages = {141--162},
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     number = {1},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2011__34_1_a0/}
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Boltje, Robert; Hartmann, Robert. Permutation resolutions for Specht modules.. Journal of Algebraic Combinatorics, Tome 34 (2011) no. 1, pp. 141-162. http://geodesic.mathdoc.fr/item/JAC_2011__34_1_a0/