The Newton polytope of the Kronecker product
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866916672209682432 |
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| author | Panova, Greta Zhao, Chenchen |
| author_facet | Panova, Greta Zhao, Chenchen |
| contents | We study the Kronecker product of two Schur functions $s_λ\ast s_μ$, defined as the image of the characteristic map of the product of two $S_n$ irreducible characters. We prove special cases of a conjecture of Monical--Tokcan--Yong that its monomial expansion has a saturated Newton polytope. Our proofs employ the Horn inequalities for positivity of Littlewood-Richardson coefficients and imply necessary conditions for the positivity of Kronecker coefficients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_10276 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Newton polytope of the Kronecker product Panova, Greta Zhao, Chenchen Combinatorics Representation Theory 05E10, 20C30 We study the Kronecker product of two Schur functions $s_λ\ast s_μ$, defined as the image of the characteristic map of the product of two $S_n$ irreducible characters. We prove special cases of a conjecture of Monical--Tokcan--Yong that its monomial expansion has a saturated Newton polytope. Our proofs employ the Horn inequalities for positivity of Littlewood-Richardson coefficients and imply necessary conditions for the positivity of Kronecker coefficients. |
| title | The Newton polytope of the Kronecker product |
| topic | Combinatorics Representation Theory 05E10, 20C30 |
| url | https://arxiv.org/abs/2311.10276 |