Braided Gelfand-Zetlin algebras and their semiclassical counterparts

2025/07/06 by Gurevich, Dimitry, Saponov, Pavel
#17B37 (Primary) #81R50 (Secondary) #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2507.04564

Abstract

We construct analogs of the Gelfand-Zetlin algebras in the Reflection Equation algebras, corresponding to Hecke symmetries, mainly to those coming from the quantum groups U_q(sl(N)). Corresponding semiclassical (i.e. Poisson) counterparts of the Gelfand-Zetlin algebras are described.

Citations

• Quantum Schur-Weyl duality and q-Frobenius formula related to Reflection Equation algebras
• From Reflection Equation Algebra to Braided Yangians
• Representation theory of (modified) Reflection Equation Algebra of GL(m|n) type
• Double quantization on coadjoint representations of simple Lie groups and its orbits
• Glueing operation for r-matrices, quantum groups and link-invariants of Hecke type

Related

• Representation theory of (modified) Reflection Equation Algebra of GL(m|n) type
• Braided modules and reflection equations
• From Reflection Equation Algebra to Braided Yangians
• Presentations for small reflection equation algebras of type A
• Braided Symmetric and Exterior Algebras