A determinantal formula for orthosymplectic Schur functions
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914935347347456 |
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| author | Kumari, Nishu |
| author_facet | Kumari, Nishu |
| contents | We prove a new determinantal formula for the characters of irreducible representations of orthosymplectic Lie superalgebras analogous to the formula developed by Moens and Jeugt (J. Algebraic Combin., 2003) for general linear Lie superalgebras. Our proof uses the Jacobi--Trudi type formulas for orthosymplectic characters. As a consequence, we show that the odd symplectic characters introduced by Proctor (Invent. Math., 1988) are the same as the orthosymplectic characters with some specialized indeterminates. We also give a generalization of an odd symplectic character identity due to Brent, Krattenthaler and Warnaar (J. Combin. Theory Ser. A, 2016). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_01723 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A determinantal formula for orthosymplectic Schur functions Kumari, Nishu Combinatorics Representation Theory 05E05, 05E10 We prove a new determinantal formula for the characters of irreducible representations of orthosymplectic Lie superalgebras analogous to the formula developed by Moens and Jeugt (J. Algebraic Combin., 2003) for general linear Lie superalgebras. Our proof uses the Jacobi--Trudi type formulas for orthosymplectic characters. As a consequence, we show that the odd symplectic characters introduced by Proctor (Invent. Math., 1988) are the same as the orthosymplectic characters with some specialized indeterminates. We also give a generalization of an odd symplectic character identity due to Brent, Krattenthaler and Warnaar (J. Combin. Theory Ser. A, 2016). |
| title | A determinantal formula for orthosymplectic Schur functions |
| topic | Combinatorics Representation Theory 05E05, 05E10 |
| url | https://arxiv.org/abs/2401.01723 |