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Modified Traces on Deligne's Category Rep(S_{t})

By Jonathan Comes and Jonathan R. Kujawa

Abstract

Deligne has defined a category which interpolates among the representations of the various symmetric groups. In this paper we show Deligne's category admits a unique nontrivial family of modified trace functions. Such modified trace functions have already proven to be interesting in both low-dimensional topology and representation theory. We also introduce a graded variant of Deligne's category, lift the modified trace functions to the graded setting, and use them to recover the well-known invariant of framed knots known as the writhe.Comment: 17 pages, 19 figure

Topics: Mathematics - Representation Theory, 18D10, 20C30
Year: 2011
OAI identifier: oai:arXiv.org:1103.2082
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