Permutation resolutions for Specht modules.

Boltje, Robert ; Hartmann, Robert

Journal of Algebraic Combinatorics, Tome 34 (2011) no. 1, pp. 141-162.

Résumé

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.

Détail

Classification : !!par!!, link, to, page, 11, link, to, page, 12, link, to, page, 12, link, to, page, 8, link, to, page, 18, link, to, page, 11, link, to, page, 12, J, Algebr, Comb, (2011), 34:, 141-162
Mots-clés : keywords symmetric group, permutation module, Specht module, resolution