REPRESENTATION THEORY IN COMPLEX RANK, I

By Pavel Etingof. Transformation groups, 2014

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P. Deligne defined interpolations of the tensor category of representations of the symmetric group Sn to complex values of n. Namely, he defined tensor categories Rep(St) for any complex t. This construction was generalized by F. Knop to the case of wreath products of Sn with a finite group. Generalizing these results, we propose a method of interpolating representation categories of various algebras containing Sn (such as degenerate affine Hecke algebras, symplectic reflection algebras, rational Cherednik algebras, etc.) to complex values of n. We also define the group algebra of Sn for complex n, study its properties, and propose a Schur-Weyl duality for Rep(St).

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/45bdaf03bb23ebfd2e70d614cba9ea7e78665235

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Citations in the corpus

FI-modules: a new approach to stability for S_n-representations (2012, background): “• Objects in Deligne’s category Rep(St), where t is a complex number, are closely related to sequences of Sn-representations whose characters are eventually polynomial (see Deligne [De], Knop [Kn], or Etingof’s lecture [Et]).”
FI-modules and stability for representations of symmetric groups (2012, background): “• Objects in Deligne’s category Rep(St), where t is a complex number, are closely related to sequences of Sn-representations whose characters are polynomial (see Deligne [De], Knop [Kn], or Etingof’s lecture [Et]).”