Basic monodromy operator for quantum superalgebra

2024/09/17 by A. V. Razumov, Razumov, A. V.
Computer Science · Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Matrix Theory and Algorithms #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2409.11097

openalex publication_date 2024/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We derive the explicit form of the basic monodromy operator for the quantum loop superalgebra U_q(L(\mathfraksl_2|1)). Two significant additional results emerge from this derivation: simple expressions for the generating functions of the the images of the root vectors of U_q(L(\mathfraksl_2|1)) under the Jimbo homomorphism and explicit expressions for certain central elements of the quantum superalgebra U_q(\mathfrakgl_2|1). Furthermore, we establish the relationship between these central elements and those obtained by using the Drinfeld partial trace method.

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