Journal of Algebraic Combinatorics

, Volume 34, Issue 1, pp 141–162

Permutation resolutions for Specht modules

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


For every composition λ of a positive integer r, we construct a finite chain complex whose terms are direct sums of permutation modules Mμ 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 Sλ. We prove the exactness in special cases.


Symmetric groupPermutation moduleSpecht moduleResolution
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© The Author(s) 2010

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaSanta CruzUSA
  2. 2.Department of MathematicsUniversity of StuttgartStuttgartGermany