The Ring of Polynomial Functors of Prime Degree

Alexander Zimmermann (1)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée

Let $\hat\Z_p$ be the ring of $p$-adic integers. We prove in the present paper that the category of polynomial functors from finitely generated free abelian groups to $\hat \Z_p$-modules of degree at most $p$ is equivalent to the category of finitely generated modules over a particularly well understood ring, called Green order. That this is the case was conjectured by Yuri Drozd.

Mots clés: Polynomial functors; Green orders; Brauer tree algebras; Schur algebras; Recollement diagram; Representation type

Domaines: Théorie des représentations [math.RT]; Topologie algébrique [math.AT]; Théorie des groupes [math.GR]

Alexander Zimmermann. The Ring of Polynomial Functors of Prime Degree. Transactions of the American Mathematical Society, Series B, 2015, 367 (10), pp.7161-7192. ⟨hal-00814553v2⟩