Combinatorial Howe duality of symplectic type

Autor:	Taehyeok Heo, Jae-Hoon Kwon
Rok vydání:	2022
Předmět:	Mathematics::Combinatorics Algebra and Number Theory 17B37 22E46 05E10 Mathematics - Quantum Algebra FOS: Mathematics Quantum Algebra (math.QA) Representation Theory (math.RT) Mathematics::Representation Theory Mathematics - Representation Theory
Zdroj:	Journal of Algebra. 600:1-44
ISSN:	0021-8693
DOI:	10.1016/j.jalgebra.2022.01.037
Popis:	We give a new combinatorial interpretation of Howe dual pairs of the form $(\g,{\rm Sp}_{2\ell})$, where $\g$ is a Lie (super)algebra of classical type. This is done by establishing a symplectic analogue of the RSK algorithm associated to this pair, in a uniform way which does not depend on $\g$. We introduce an analogue of jeu de taquin sliding for spinor model of irreducible characters of a Lie superalgebra $\g$ to define $P$-tableau and show that the associated $Q$-tableau is given by a symplectic tableau due to King. 38 pages
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e34d66ad391804d1717654680fd94f5b https://doi.org/10.1016/j.jalgebra.2022.01.037 Zobrazit plný text záznamu Full Text from ScienceDirect