q-deformed Howe duality for orthosymplectic Lie superalgebras

2025/06/06 by Jeong Ja Bae, Bae, Jeong, Jae-Hoon Kwon +1 · 1 citation
Mathematics · #17B10 #17B37 #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2506.05959

openalex publication_date 2025/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a q-analogue of Howe duality associated to a pair (\mfg,G), where \mfg is an orthosymplectic Lie superalgebra and G=O_ℓ, Sp_2ℓ. We define explicitly commuting actions of a quantized enveloping algebra of \mfg and the \imathquantum group of type AI and AII on a q-deformed supersymmetric space, and describe its semisimple decomposition whose classical limit recovers the (\mfg,G)-duality. As special cases, we obtain q-analogues of (\mfg,G)-dualities on symmetric and exterior algebras for \mfg=\mfso_2n, \mfsp_2n.

Citations

• Quantum supersymmetric pairs of basic types
• Oscillator representations of quantum affine orthosymplectic superalgebras
• A new tableau model for irreducible polynomial representations of the orthogonal group
• Based modules over the \imathquantum group of type AI
• Dualities for spin representations
• R matrix for generalized quantum group of type A
• Howe Duality and Combinatorial Character Formula for Orthosymplectic Lie superalgebras
• Lie subalgebras of differential operators on the super circle
• Crystal Bases for the Quantum Superalgebra U_q(gl(m,n))
• Duality in infinite dimensional Fock representations
• Macdonald's symmetric polynomials as zonal spherical functions on some\n quantum homogeneous spaces
• Q-analogues of Clifford and Weyl algebras-spinor and oscillator representations of quantum enveloping algebras

Cited by

• Quantum Howe duality and Schur duality of type AIII

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