A solution of the 3D reflection equation from quantized algebra of functions of type B
Atsuo Kuniba, Masato Okado
TL;DR
This paper constructs a new solution to the 3D reflection equation by embedding the quantized algebra of functions of type B into type C and combining it with previous solutions, advancing the understanding of quantum algebra symmetries.
Contribution
It explicitly embeds the quantized algebra of functions of type B into type C and uses this to derive a novel solution to the 3D reflection equation.
Findings
Explicit embedding of A_q(B_2) into A_q(C_2)
New solution to the 3D reflection equation
Application of algebraic embedding to quantum integrable systems
Abstract
Let A_q(g) be the quantized algebra of functions associated with simple Lie algebra g defined by generators obeying the so called RTT relations. We describe the embedding explicitly. As an application, a new solution of the Isaev-Kulish 3D reflection equation is constructed by combining the embedding with the previous solution for A_q(C_2) by the authors.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Advanced Algebra and Geometry