Revisiting Jacobi-Trudi identities via the BGG category $\mathcal{O}$
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866912112158179328 |
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| author | Gui, Tao Yang, Arthur L. B. |
| author_facet | Gui, Tao Yang, Arthur L. B. |
| contents | By interpreting Kostka numbers as tensor product multiplicities in the BGG category O for the special linear Lie algebras, we provide a new proof of the classical Jacobi--Trudi identities for skew Schur polynomials, derived from the celebrated Weyl character formula. We re-establish the Schur positivity of certain truncations in the Jacobi--Trudi expansion of skew Schur polynomials and obtain Schur positivity results for similar truncations in the Jacobi--Trudi-type expansion of the product of two Schur polynomials. Furthermore, we interpret the coefficients in the Schur polynomial expansions of these Jacobi--Trudi truncations as tensor product multiplicities in the BGG category O. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_12632 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Revisiting Jacobi-Trudi identities via the BGG category $\mathcal{O}$ Gui, Tao Yang, Arthur L. B. Representation Theory Combinatorics 05E05, 05E10, 17B10, 17B20, 18G10 By interpreting Kostka numbers as tensor product multiplicities in the BGG category O for the special linear Lie algebras, we provide a new proof of the classical Jacobi--Trudi identities for skew Schur polynomials, derived from the celebrated Weyl character formula. We re-establish the Schur positivity of certain truncations in the Jacobi--Trudi expansion of skew Schur polynomials and obtain Schur positivity results for similar truncations in the Jacobi--Trudi-type expansion of the product of two Schur polynomials. Furthermore, we interpret the coefficients in the Schur polynomial expansions of these Jacobi--Trudi truncations as tensor product multiplicities in the BGG category O. |
| title | Revisiting Jacobi-Trudi identities via the BGG category $\mathcal{O}$ |
| topic | Representation Theory Combinatorics 05E05, 05E10, 17B10, 17B20, 18G10 |
| url | https://arxiv.org/abs/2209.12632 |