Block characters of the symmetric groups
A block character of a finite symmetric group is a positive definite function which depends only on the number of cycles in a permutation. We describe the cone of block characters by identifying its extreme rays, and find relations of the characters to descent representations and the coinvariant alg...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Springer US
2016
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| Online Access: | http://hdl.handle.net/1721.1/105432 https://orcid.org/0000-0002-9828-5862 |
| _version_ | 1826197054765924352 |
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| author | Gnedin, Alexander Gorin, Vadim Kerov, Sergei |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Gnedin, Alexander Gorin, Vadim Kerov, Sergei |
| author_sort | Gnedin, Alexander |
| collection | MIT |
| description | A block character of a finite symmetric group is a positive definite function which depends only on the number of cycles in a permutation. We describe the cone of block characters by identifying its extreme rays, and find relations of the characters to descent representations and the coinvariant algebra of S[subscript n]. The decomposition of extreme block characters into the sum of characters of irreducible representations gives rise to certain limit shape theorems for random Young diagrams. We also study counterparts of the block characters for the infinite symmetric group S[subscript n], along with their connection to the Thoma characters of the infinite linear group GL[subscript ∞](q) over a Galois field. |
| first_indexed | 2024-09-23T10:42:06Z |
| format | Article |
| id | mit-1721.1/105432 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T10:42:06Z |
| publishDate | 2016 |
| publisher | Springer US |
| record_format | dspace |
| spelling | mit-1721.1/1054322022-09-30T22:22:24Z Block characters of the symmetric groups Gnedin, Alexander Gorin, Vadim Kerov, Sergei Massachusetts Institute of Technology. Department of Mathematics Gorin, Vadim A block character of a finite symmetric group is a positive definite function which depends only on the number of cycles in a permutation. We describe the cone of block characters by identifying its extreme rays, and find relations of the characters to descent representations and the coinvariant algebra of S[subscript n]. The decomposition of extreme block characters into the sum of characters of irreducible representations gives rise to certain limit shape theorems for random Young diagrams. We also study counterparts of the block characters for the infinite symmetric group S[subscript n], along with their connection to the Thoma characters of the infinite linear group GL[subscript ∞](q) over a Galois field. 2016-11-22T20:48:41Z 2016-11-22T20:48:41Z 2012-08 2012-02 2016-08-18T15:42:23Z Article http://purl.org/eprint/type/JournalArticle 0925-9899 1572-9192 http://hdl.handle.net/1721.1/105432 Gnedin, Alexander, Vadim Gorin, and Sergei Kerov. “Block Characters of the Symmetric Groups.” Journal of Algebraic Combinatorics 38.1 (2013): 79–101. https://orcid.org/0000-0002-9828-5862 en http://dx.doi.org/10.1007/s10801-012-0394-9 Journal of Algebraic Combinatorics Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. Springer Science+Business Media, LLC application/pdf Springer US Springer US |
| spellingShingle | Gnedin, Alexander Gorin, Vadim Kerov, Sergei Block characters of the symmetric groups |
| title | Block characters of the symmetric groups |
| title_full | Block characters of the symmetric groups |
| title_fullStr | Block characters of the symmetric groups |
| title_full_unstemmed | Block characters of the symmetric groups |
| title_short | Block characters of the symmetric groups |
| title_sort | block characters of the symmetric groups |
| url | http://hdl.handle.net/1721.1/105432 https://orcid.org/0000-0002-9828-5862 |
| work_keys_str_mv | AT gnedinalexander blockcharactersofthesymmetricgroups AT gorinvadim blockcharactersofthesymmetricgroups AT kerovsergei blockcharactersofthesymmetricgroups |