Necessary conditions for the positivity of Littlewood–Richardson and plethystic coefficients
We give necessary conditions for the positivity of Littlewood–Richardson coefficients and SXP coefficients. We deduce necessary conditions for the positivity of the plethystic coefficients. Explicitly, our main result states that if $S^\lambda (V)$ appears as a summand in the decomposition into irre...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2023-10-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.468/ |
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| author | Gutiérrez, Álvaro Rosas, Mercedes H. |
| author_facet | Gutiérrez, Álvaro Rosas, Mercedes H. |
| author_sort | Gutiérrez, Álvaro |
| collection | DOAJ |
| description | We give necessary conditions for the positivity of Littlewood–Richardson coefficients and SXP coefficients. We deduce necessary conditions for the positivity of the plethystic coefficients. Explicitly, our main result states that if $S^\lambda (V)$ appears as a summand in the decomposition into irreducibles of $S^\mu (S^\nu (V))$, then $\nu $’s diagram is contained in $\lambda $’s diagram. |
| format | Article |
| id | doaj-art-c4db1de5d5d642c9a6fb3a0f29852152 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-10-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-c4db1de5d5d642c9a6fb3a0f298521522025-02-07T11:09:55ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-10-01361G71163117310.5802/crmath.46810.5802/crmath.468Necessary conditions for the positivity of Littlewood–Richardson and plethystic coefficientsGutiérrez, Álvaro0https://orcid.org/0000-0003-0746-5794Rosas, Mercedes H.1https://orcid.org/0000-0002-7738-5792Universidad de Sevilla, SpainUniversidad de Sevilla, SpainWe give necessary conditions for the positivity of Littlewood–Richardson coefficients and SXP coefficients. We deduce necessary conditions for the positivity of the plethystic coefficients. Explicitly, our main result states that if $S^\lambda (V)$ appears as a summand in the decomposition into irreducibles of $S^\mu (S^\nu (V))$, then $\nu $’s diagram is contained in $\lambda $’s diagram.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.468/ |
| spellingShingle | Gutiérrez, Álvaro Rosas, Mercedes H. Necessary conditions for the positivity of Littlewood–Richardson and plethystic coefficients Comptes Rendus. Mathématique |
| title | Necessary conditions for the positivity of Littlewood–Richardson and plethystic coefficients |
| title_full | Necessary conditions for the positivity of Littlewood–Richardson and plethystic coefficients |
| title_fullStr | Necessary conditions for the positivity of Littlewood–Richardson and plethystic coefficients |
| title_full_unstemmed | Necessary conditions for the positivity of Littlewood–Richardson and plethystic coefficients |
| title_short | Necessary conditions for the positivity of Littlewood–Richardson and plethystic coefficients |
| title_sort | necessary conditions for the positivity of littlewood richardson and plethystic coefficients |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.468/ |
| work_keys_str_mv | AT gutierrezalvaro necessaryconditionsforthepositivityoflittlewoodrichardsonandplethysticcoefficients AT rosasmercedesh necessaryconditionsforthepositivityoflittlewoodrichardsonandplethysticcoefficients |