Weyl modules for queer Lie superalgebras

2023/02/28 by Saudamini Nayak, Nayak, Saudamini · 1 citation
Mathematics · #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.2302.14787

openalex publication_date 2023/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define global and local Weyl modules for q ⊗ A, where q is the queer Lie superalgebra and A is an associative commutative unital ℂ-algebra. We prove that global Weyl modules are universal highest weight objects in certain category upto parity reversing functor Π. Then with the assumption that A is finitely generated and with a special technical condition which simple root system of q satisfy it is shown that the local Weyl modules are finite dimensional. Further they are universal highest map-weight objects in certain category upto Π. Finally we prove a tensor product property for local Weyl modules.

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