Deligne categories and reduced Kronecker coefficients
The Kronecker coefficients are the structural constants for the tensor categories of representations of the symmetric groups, namely, given three partitions λ,μ,τ of n, the multiplicity of λ in μ⊗τ is called the Kronecker coefficient g[superscript λ][subscript μ,τ]. When the first part of each of th...
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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/1721.1/105783 https://orcid.org/0000-0002-0226-1859 |
| _version_ | 1811071037047046144 |
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| author | Entova-Aizenbud, Inna |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Entova-Aizenbud, Inna |
| author_sort | Entova-Aizenbud, Inna |
| collection | MIT |
| description | The Kronecker coefficients are the structural constants for the tensor categories of representations of the symmetric groups, namely, given three partitions λ,μ,τ of n, the multiplicity of λ in μ⊗τ is called the Kronecker coefficient g[superscript λ][subscript μ,τ]. When the first part of each of the partitions is taken to be very large (the remaining parts being fixed), the values of the appropriate Kronecker coefficients stabilize; the stable value is called the reduced (or stable) Kronecker coefficient. These coefficients also generalize the Littlewood–Richardson coefficients and have been studied quite extensively. In this paper, we show that reduced Kronecker coefficients appear naturally as structure constants of Deligne categories [bar under Rep](S[subscript t]). This allows us to interpret various properties of the reduced Kronecker coefficients as categorical properties of Deligne categories [bar under Rep](S[subscript t]) and derive new combinatorial identities. |
| first_indexed | 2024-09-23T08:45:09Z |
| format | Article |
| id | mit-1721.1/105783 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T08:45:09Z |
| publishDate | 2016 |
| publisher | Springer US |
| record_format | dspace |
| spelling | mit-1721.1/1057832022-09-30T11:00:30Z Deligne categories and reduced Kronecker coefficients Entova-Aizenbud, Inna Massachusetts Institute of Technology. Department of Mathematics Entova-Aizenbud, Inna The Kronecker coefficients are the structural constants for the tensor categories of representations of the symmetric groups, namely, given three partitions λ,μ,τ of n, the multiplicity of λ in μ⊗τ is called the Kronecker coefficient g[superscript λ][subscript μ,τ]. When the first part of each of the partitions is taken to be very large (the remaining parts being fixed), the values of the appropriate Kronecker coefficients stabilize; the stable value is called the reduced (or stable) Kronecker coefficient. These coefficients also generalize the Littlewood–Richardson coefficients and have been studied quite extensively. In this paper, we show that reduced Kronecker coefficients appear naturally as structure constants of Deligne categories [bar under Rep](S[subscript t]). This allows us to interpret various properties of the reduced Kronecker coefficients as categorical properties of Deligne categories [bar under Rep](S[subscript t]) and derive new combinatorial identities. 2016-12-09T19:32:26Z 2016-12-09T19:32:26Z 2016-02 2014-10 2016-08-18T15:42:27Z Article http://purl.org/eprint/type/JournalArticle 0925-9899 1572-9192 http://hdl.handle.net/1721.1/105783 Entova Aizenbud, Inna. “Deligne Categories and Reduced Kronecker Coefficients.” Journal of Algebraic Combinatorics 44.2 (2016): 345–362. https://orcid.org/0000-0002-0226-1859 en http://dx.doi.org/10.1007/s10801-016-0672-z 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 New York application/pdf Springer US Springer US |
| spellingShingle | Entova-Aizenbud, Inna Deligne categories and reduced Kronecker coefficients |
| title | Deligne categories and reduced Kronecker coefficients |
| title_full | Deligne categories and reduced Kronecker coefficients |
| title_fullStr | Deligne categories and reduced Kronecker coefficients |
| title_full_unstemmed | Deligne categories and reduced Kronecker coefficients |
| title_short | Deligne categories and reduced Kronecker coefficients |
| title_sort | deligne categories and reduced kronecker coefficients |
| url | http://hdl.handle.net/1721.1/105783 https://orcid.org/0000-0002-0226-1859 |
| work_keys_str_mv | AT entovaaizenbudinna delignecategoriesandreducedkroneckercoefficients |