Oscillator representations of quantum affine orthosymplectic superalgebras

2023/04/13 by Jae-Hoon Kwon, Kwon, Jae-Hoon, Sin-Myung Lee +3 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2304.06215

openalex publication_date 2023/04/13 · openalex created_date 2023/04/15 · openalex updated_date 2026/07/28

Abstract

We introduce a category of q-oscillator representations over the quantum affine superalgebras of type D and construct a new family of its irreducible representations. Motivated by the theory of super duality, we show that these irreducible representations naturally interpolate the irreducible q-oscillator representations of type X_n⁽¹⁾ and the finite-dimensional irreducible representations of type Y_n⁽¹⁾ for (X,Y)=(C,D),(D,C) under exact monoidal functors. This can be viewed as a quantum (untwisted) affine analogue of the correspondence between irreducible oscillator and irreducible finite-dimensional representations of classical Lie algebras arising from Howe's reductive dual pairs (\mathfrakg,G), where \mathfrakg=\mathfraksp_2n, \mathfrakso_2n and G=O_ℓ, Sp_2ℓ.

Cited by

• q-deformed Howe duality for orthosymplectic Lie superalgebras

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