Commuting Families of Flag Quasideterminants in Reflection Equation Algebras of Type A

Dmitry V. Talalaev

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arXiv · 2610.32521

Commuting Families of Flag Quasideterminants in Reflection Equation Algebras of Type A

Dmitry V. Talalaev

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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.

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Dmitry V. Talalaev. 2026-10-23. Commuting Families of Flag Quasideterminants in Reflection Equation Algebras of Type A. https://arxiv.org/abs/2610.32521

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