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...
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Springer-Verlag
2015
|
| Online Access: | http://hdl.handle.net/1721.1/92855 https://orcid.org/0000-0002-0710-1416 |
| _version_ | 1826210210279063552 |
|---|---|
| author | Etingof, Pavel I. |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Etingof, Pavel I. |
| author_sort | Etingof, Pavel I. |
| collection | MIT |
| description | 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]). |
| first_indexed | 2024-09-23T14:45:23Z |
| format | Article |
| id | mit-1721.1/92855 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T14:45:23Z |
| publishDate | 2015 |
| publisher | Springer-Verlag |
| record_format | dspace |
| spelling | mit-1721.1/928552022-09-29T10:22:54Z Representation Theory in Complex Rank, I Etingof, Pavel I. Massachusetts Institute of Technology. Department of Mathematics Etingof, Pavel 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[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) 2015-01-14T16:45:51Z 2015-01-14T16:45:51Z 2014-03 2014-01 Article http://purl.org/eprint/type/JournalArticle 1083-4362 1531-586X http://hdl.handle.net/1721.1/92855 Etingof, Pavel. “Representation Theory in Complex Rank, I.” Transformation Groups 19, no. 2 (March 25, 2014): 359–381. https://orcid.org/0000-0002-0710-1416 en_US http://dx.doi.org/10.1007/s00031-014-9260-2 Transformation Groups Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Springer-Verlag arXiv |
| spellingShingle | Etingof, Pavel I. Representation Theory in Complex Rank, I |
| title | Representation Theory in Complex Rank, I |
| title_full | Representation Theory in Complex Rank, I |
| title_fullStr | Representation Theory in Complex Rank, I |
| title_full_unstemmed | Representation Theory in Complex Rank, I |
| title_short | Representation Theory in Complex Rank, I |
| title_sort | representation theory in complex rank i |
| url | http://hdl.handle.net/1721.1/92855 https://orcid.org/0000-0002-0710-1416 |
| work_keys_str_mv | AT etingofpaveli representationtheoryincomplexranki |