Representation Theory in Complex Rank, I
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[sub...
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| Format: | Article |
| Language: | English |
| Published: |
Springer-Verlag,
2015-01-14T16:45:51Z.
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| Online Access: | Get fulltext |
| Summary: | 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]). National Science Foundation (U.S.) (Grant DMS-0504847) National Science Foundation (U.S.) (Grant DMS-1000113) |
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