nLab
Specht module

Contents

Contents

Idea

Specht modules are linear representations of the symmetric group Sym(n)Sym(n) (for any \in \mathbb{N}), hence modules over the group ring k(Sym(n))k(Sym(n)), which are indexed by the partitions of nn. In characteristic 0, they are irreducible and exhaust the isomorphism classes of irreps (e.g. Sagan 01, Thm. 2.4.6).

Over a field of positive characteristic pp, where pn!p \mid n!, the Specht modules are not irreducible, but every irreducible module does appear as the cosocle of a Specht module.

References

Textbook accounts:

See also

Last revised on April 29, 2021 at 01:34:48. See the history of this page for a list of all contributions to it.