Representation theory of the reflection equation algebra III: Classification of irreducible representations

2025/06/20 by Moore, Stephen T.
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2506.16866

openalex publication_date 2025/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We continue our study of Hilbert space representations of the Reflection Equation Algebra, again focusing on the algebra constructed from the R-matrix associated to the q-deformation of GL(N,ℂ) for 0

Citations

• Representation theory of the Reflection Equation Algebra II: Theory of shapes
• The center of the reflection equation algebra via quantum minors
• Reflection equation algebras, coideal subalgebras, and their centres
• On quantization of Semenov-Tian-Shansky Poisson bracket on simple algebraic groups
• On universal solution to reflection equation
• The Quantum Double as Quantum Mechanics

Related

• Representation theory of the Reflection Equation Algebra II: Theory of shapes
• Representation theory of the reflection equation algebra I: A quantization of Sylvester's law of inertia
• Characters of \U_q(gl(n))-reflection equation algebra
• Diagonal reduction algebra and reflection equation
• Representation theory of (modified) Reflection Equation Algebra of GL(m|n) type