Skew symplectic and orthogonal characters through lattice paths

Autor:	Albion, Seamus P., Fischer, Ilse, Höngesberg, Hans, Schreier-Aigner, Florian
Rok vydání:	2023
Předmět:	Mathematics - Combinatorics Mathematics - Representation Theory 05A05 05A15 05A19 05E05 05E10 05E16 20G05
Zdroj:	European Journal of Combinatorics 122 (2024), 104000
Druh dokumentu:	Working Paper
DOI:	10.1016/j.ejc.2024.104000
Popis:	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. Comment: 30 pages, 16 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2305.11730 Zobrazit plný text záznamu View this record from Arxiv