Skew symplectic and orthogonal characters through lattice paths
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866916324889853952 |
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| author | Albion, Seamus P. Fischer, Ilse Höngesberg, Hans Schreier-Aigner, Florian |
| author_facet | Albion, Seamus P. Fischer, Ilse Höngesberg, Hans Schreier-Aigner, Florian |
| contents | The skew Schur functions admit many determinantal expressions. Chief among them are the (dual) Jacobi-Trudi formula and the Lascoux-Pragacz formula, which is a skew analogue of the Giambelli identity. Comparatively, the skew characters of the symplectic and orthogonal groups, also known as the skew symplectic and orthogonal Schur functions, have received less attention in this direction. We establish analogues of the dual Jacobi-Trudi and Lascoux-Pragacz formulae for these characters. Our approach is entirely combinatorial, being based on lattice path descriptions of the tableaux models of Koike and Terada. Ordinary Jacobi-Trudi formulae are then derived in an algebraic manner from their duals. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2305_11730 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Skew symplectic and orthogonal characters through lattice paths Albion, Seamus P. Fischer, Ilse Höngesberg, Hans Schreier-Aigner, Florian Combinatorics Representation Theory 05A05, 05A15, 05A19, 05E05, 05E10, 05E16, 20G05 The skew Schur functions admit many determinantal expressions. Chief among them are the (dual) Jacobi-Trudi formula and the Lascoux-Pragacz formula, which is a skew analogue of the Giambelli identity. Comparatively, the skew characters of the symplectic and orthogonal groups, also known as the skew symplectic and orthogonal Schur functions, have received less attention in this direction. We establish analogues of the dual Jacobi-Trudi and Lascoux-Pragacz formulae for these characters. Our approach is entirely combinatorial, being based on lattice path descriptions of the tableaux models of Koike and Terada. Ordinary Jacobi-Trudi formulae are then derived in an algebraic manner from their duals. |
| title | Skew symplectic and orthogonal characters through lattice paths |
| topic | Combinatorics Representation Theory 05A05, 05A15, 05A19, 05E05, 05E10, 05E16, 20G05 |
| url | https://arxiv.org/abs/2305.11730 |