Journal of Algebraic Combinatorics

, Volume 34, Issue 1, pp 141–162

Permutation resolutions for Specht modules

Authors

    • Department of MathematicsUniversity of California
  • Robert Hartmann
    • Department of MathematicsUniversity of Stuttgart
Open AccessArticle

DOI: 10.1007/s10801-010-0265-1

Cite this article as:
Boltje, R. & Hartmann, R. J Algebr Comb (2011) 34: 141. doi:10.1007/s10801-010-0265-1

Abstract

For every composition λ of a positive integer r, we construct a finite chain complex whose terms are direct sums of permutation modules M μ for the symmetric group \(\mathfrak{S}_{r}\) with Young subgroup stabilizers \(\mathfrak{S}_{\mu}\). The construction is combinatorial and can be carried out over every commutative base ring k. We conjecture that for every partition λ 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 λ . We prove the exactness in special cases.

Keywords

Symmetric group Permutation module Specht module Resolution

Copyright information

© The Author(s) 2010