Year: 2026
Type: preprint
Abstract: We consider a family of northeastern antidiagonal quasideterminants associated with the successive blocks of the generating matrix of a reflection equation (RE) algebra of type $A_{n-1}$. Our main result proves the conjecture on their pairwise commutativity formulated earlier. The proof uses the triangular realization of the RE algebra in a quantum enveloping algebra and the flag property of quasideterminants. We also discuss the interpretation of these elements in terms of quantum cluster coordinates and their possible connection with generalized Toda systems.
Source: arXiv (Cornell University)
Author: Talalaev, Dmitry V.
Institutions: Yaroslavl State University, Lomonosov Moscow State University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223682377