Representation theory in complex rank, II

2014/07/01 by Etingof, Pavel · 2 citations
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1407.0373

Abstract

This paper is a sequel to arXiv:1401.6321. We define and study representation categories based on Deligne categories Rep(GL_t), Rep(O_t), Rep(Sp₂t), where t is any (non-integer) complex number. Namely, we define complex rank analogs of the parabolic category O and the representation categories of real reductive Lie groups and supergroups, affine Lie algebras, and Yangians. We develop a framework and language for studying these categories, prove basic results about them, and outline a number of directions of further research.

Cited by

• Vogel's universality and the classification problem for Jacobi identities
• Harish-Chandra bimodules in the Deligne category Rep(GL_t)

Related

• Representation theory in complex rank, I
• Finite-dimensional representations of Yangians in complex rank
• Certain complex representations of SL₂(\mathbbF_q)
• Representation Theory of the Twisted Yangians in Complex Rank
• Deligne categories as limits in rank and characteristic