Simple commutative algebras in Deligne's categories Rep(S_t)

2015/06/24 by Luke Sciarappa, Sciarappa, Luke · 4 citations
Mathematics · #Algebraic structures and combinatorial models #Advanced Algebra and Geometry #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.1506.07565

Abstract

We show that in the Deligne categories Rep(S_t) for t a transcendental number, the only simple algebra objects are images of simple algebras in the category of representations of a symmetric group under a canonical induction functor. They come in families which interpolate the families of algebras of functions on the cosets of H× S_n-k in S_n, for a fixed subgroup H of S_k.

Cited by

• Classification of simple algebras in Deligne category Rep(S_t)
• Classification of simple commutative algebras in the Delannoy category
• Harish-Chandra bimodules of finite K-type in Deligne categories
• Deligne categories as limits in rank and characteristic

Related

• Classification of simple algebras in Deligne category Rep(S_t)
• Deligne categories and representations of the infinite symmetric group
• Representation theory in complex rank, I
• Integral objects and Deligne's category Rep(S_t)
• An Introduction to Deligne Categories