PreprintCC BY 4.0arXiv
Commuting Families of Flag Quasideterminants in Reflection Equation Algebras of Type A
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 An−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.
Related
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BibTeX
@misc{talalaev2026commuting,
title = {{Commuting Families of Flag Quasideterminants in Reflection Equation Algebras of Type A}},
author = {Dmitry V. Talalaev},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32521},
eprint = {2610.32521},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32521},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Commuting Families of Flag Quasideterminants in Reflection Equation Algebras of Type A
AU - Dmitry V. Talalaev
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32521
UR - https://arxiv.org/abs/2610.32521
AB - 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.
ER -