Symmetric powers, indecomposables and representation stability

Geoffrey Powell (1)

1 LAREMA - Laboratoire Angevin de Recherche en Mathématiques

Working over the prime field F_p, the structure of the indecomposables Q^* for the action of the algebra of Steenrod reduced powers A(p) on the symmetric power functors S^* is studied by exploiting the theory of strict polynomial functors. In particular, working at the prime 2, representation stability is exhibited for certain related functors, leading to a Conjectural representation stability description of quotients of Q^* arising from the polynomial filtration of symmetric powers.

Mots clés: Functor; strict polynomial functor; polynomial functor; highest weight category; Ringel duality; representation stability; symmetric power; indecomposable; Steenrod algebra; Peterson hit problem.

Domaines: Topologie algébrique [math.AT]

Geoffrey Powell. Symmetric powers, indecomposables and representation stability. 2018. ⟨hal-01880915⟩