Graded representations of current Lie superalgebras \mathfraksl(1|2)[t]

2025/06/01 by Shushma Rani, Rani, Shushma, Divya Setia +1
Mathematics · #05E10 #16S30 #17B05 #17B10 17B35 17B65 #17B67 #17B70 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2506.01134

openalex publication_date 2025/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is the study of finite-dimensional graded representations of current lie superalgebras \mathfraksl(1|2)[t]. We define the notion of super POPs, a combinatorial tool to provide another parametrization of the basis of the local Weyl module given in [2]. We derive the graded character formula of local Weyl module for \mathfraksl(1|2)[t]. Furthermore, we construct a short exact sequence of Chari-Venkatesh modules for \mathfraksl(1|2)[t]. As a consequence, we prove that Chari-Venkatesh modules are isomorphic to the fusion of generalized Kac modules.

Citations

• Graded Character Formula for Fusion Products of Irreducible Modules and Littlewood-Richardson Coefficients in Type A₂
• On Chari-Loktev bases for local Weyl modules in type A
• Demazure modules, Fusion products and Q--systems
• BGG reciprocity for current algebras
• Weyl Modules for Classical and Quantum Affine algebras
• On generalized Kostka polynomials and quantum Verlinde rule

Related

• Local Weyl modules and fusion products for the current superalgebra \mathfraksl(1|2)[t]
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• Representations of a class of infinite-dimensional primitive Lie superalgebras
• Categorification of generic Su-Zhang character formula
• Kazhdan-Lusztig polynomials and character formulae for the Lie superalgebra gl(m|n)