Combinatorial Howe duality of symplectic type

Taehyeok Heo; Jae-Hoon Kwon

doi:10.1016/j.jalgebra.2022.01.037

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arXiv · 2008.05093

Combinatorial Howe duality of symplectic type

Taehyeok Heo·Jae-Hoon Kwon

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Abstract

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.

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BibTeX RIS

Taehyeok Heo, Jae-Hoon Kwon. 2020-08-12. Combinatorial Howe duality of symplectic type. https://doi.org/10.1016/j.jalgebra.2022.01.037

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