Séminaire Lotharingien de Combinatoire, 85B.24 (2021), 12 pp.

Taehyeok Heo and Jae-Hoon Kwon

Combinatorial Howe Duality of Symplectic Type

Abstract. We give a symplectic analog of the RSK algorithm for Howe dual pairs of the form (g, Sp_2ℓ), where is a Lie (super)algebra of classical type. We introduce an analog of jeu de taquin sliding for spinor model of irreducible characters of a Lie superalgebra g to define P-tableau, and then define the associated Q-tableau in terms of a symplectic tableau due to King.

Received: December 1, 2020. Accepted: March 1, 2021. Final version: April 29, 2021.

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