The Quantum Super Yangian and Casimir Operators of $U_q(gl(M|N))$
R. B. Zhang
TL;DR
This paper introduces the quantum super Yangian associated with $gl(M|N)$, investigates its structure, and explicitly constructs the Casimir operators of the quantum supergroup $U_q(gl(M|N))$ through a graded algebra epimorphism.
Contribution
It provides a detailed study of the quantum super Yangian $Y_q(gl(M|N))$, including its central algebra and an explicit construction of Casimir operators for $U_q(gl(M|N))$.
Findings
Established an algebra epimorphism from $Y_q(gl(M|N))$ to $U_q(gl(M|N))$
Identified the images of central elements as Casimir operators
Analyzed the structural properties of the quantum super Yangian
Abstract
The quantum super Yangian associated with the Perk - Schultz solution of the Yang - Baxter equation is introduced. Its structural properties are investigated, in particular, an extensive study of its central algebra is carried out. A graded associative algebra epimorphism is established and constructed explicitly. Images of the central elements of the quantum super Yangian under this epimorphism yield the Casimir operators of the quantum supergroup constructed in an earlier publication.
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