Journal of Algebraic Combinatorics

, Volume 34, Issue 1, pp 141-162

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

Permutation resolutions for Specht modules

  • Robert BoltjeAffiliated withDepartment of Mathematics, University of California Email author 
  • , Robert HartmannAffiliated withDepartment of Mathematics, University of Stuttgart


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.


Symmetric group Permutation module Specht module Resolution