2020/08/31 by Taehyeok Heo, Jae-Hoon Kwon
Mathematics · #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Affine Lie algebra #Algebra over a field #Algebraic structures and combinatorial models #Combinatorics #Computer science #Current algebra #Duality (order theory) #Interpretation (philosophy) #Lie superalgebra #Mathematical physics #Mathematics #Pure mathematics #Spinor #Symplectic geometry #Type (biology) #math.QA #math.RT #msc:05E10 #msc:17B37 #msc:22E46
paper · pdf · doi:10.1016/j.jalgebra.2022.01.037
published as J. Algebra 600 (2022) 1-44 · 38 pages
openalex publication_date 2022/03/01 · arxiv created 2022/03/15 · arxiv updated 2022/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We give a new combinatorial interpretation of Howe dual pairs of the form (\g,\rm Sp2ℓ), 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.