Representation Theory in Complex Rank, I
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Etingof_Representation theory.pdf
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287.72 KB
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Author(s)
Etingof, Pavel I.
Date Issued
March 2014
Journal
Transformation Groups
Publisher
Springer-Verlag
Citation
Etingof, Pavel. “Representation Theory in Complex Rank, I.” Transformation Groups 19, no. 2 (March 25, 2014): 359–381.
Version
Author's final manuscript
Abstract
P. Deligne defined interpolations of the tensor category of representations of the symmetric group S [subscript n] to complex values of n. Namely, he defined tensor categories Rep(S [subscript t]) for any complex t. This construction was generalized by F. Knop to the case of wreath products of S[subscript n] with a finite group. Generalizing these results, we propose a method of interpolating representation categories of various algebras containing S [subscript n] (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 S [subscript n] for complex n, study its properties, and propose a Schur-Weyl duality for Rep(S [subscript t]).
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/s00031-014-9260-2
