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Advances in R-matrices and their applications (after Maulik-Okounkov, Kang-Kashiwara-Kim-Oh,...)

R-matrices are the solutions of the Yang-Baxter equation. At the origin of the quantum group theory, they may be interpreted as intertwining operators. Recent advances have been made independently in different directions. Maulik-Okounkov have given a geometric approach to R-matrices with new tools in symplectic geometry, the stable envelopes. Kang-Kashiwara-Kim-Oh proved a conjecture on the categorification of cluster algebras by using R-matrices in a crucial way. Eventually, a better understanding of the action of transfer-matrices obtained from R-matrices led to the proof of several conjectures about the corresponding quantum integrable systems.

preprint2017arXivOpen access
David Hernandez
math.RTmath-phmath.QAmath.MPmath.AGmath.RA
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Open access1 author6 topics
Imported metadata coverageMissing code, dataset, citation and institution fields are tracked without dominating the paper.Details
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