Representation theory in complex rank, II

By Pavel Etingof. 2014

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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(Sp_2t), 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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/bcedd9f7045136ad9fe717cedd8685c7b03b4ac3