Cluster algebras III: Upper bounds and double Bruhat cells
A Berenstein, S Fomin, A Zelevinsky - 2005 - projecteuclid.org
We develop a new approach to cluster algebras, based on the notion of an upper cluster
algebra defined as an intersection of Laurent polynomial rings. Strengthening the Laurent …
algebra defined as an intersection of Laurent polynomial rings. Strengthening the Laurent …
[图书][B] Cluster algebras and Poisson geometry
M Gekhtman, M Shapiro, A Vainshtein - 2010 - books.google.com
The first book devoted to cluster algebras, this work contains chapters on Poisson geometry
and Schubert varieties; an introduction to cluster algebras and their main properties; and …
and Schubert varieties; an introduction to cluster algebras and their main properties; and …
Cluster algebras and Poisson geometry
M Gekhtman, M Shapiro, A Vainshtein - arXiv preprint math/0208033, 2002 - arxiv.org
We introduce a Poisson variety compatible with a cluster algebra structure and a compatible
toric action on this variety. We study Poisson and topological properties of the union of …
toric action on this variety. We study Poisson and topological properties of the union of …
Yang–Baxter maps and integrable dynamics
AP Veselov - Physics Letters A, 2003 - Elsevier
The hierarchy of commuting maps related to a set-theoretical solution of the quantum Yang–
Baxter equation (Yang–Baxter map) is introduced. They can be considered as dynamical …
Baxter equation (Yang–Baxter map) is introduced. They can be considered as dynamical …
Multiplicative slices, relativistic Toda and shifted quantum affine algebras
M Finkelberg, A Tsymbaliuk - Representations and Nilpotent Orbits of Lie …, 2019 - Springer
We introduce the shifted quantum affine algebras. They map homomorphically into the
quantized K-theoretic Coulomb branches of 3 d N= 4 3 d {\mathcal N= 4 SUSY quiver gauge …
quantized K-theoretic Coulomb branches of 3 d N= 4 3 d {\mathcal N= 4 SUSY quiver gauge …
Loop groups, clusters, dimers and integrable systems
V Fock, A Marshakov, F Schaffhauser… - … and quantization of …, 2016 - Springer
The main idea of this work is to demonstrate the equivalence of two a priori different
methods of construction and description of a wide class of integrable models, and thus, to …
methods of construction and description of a wide class of integrable models, and thus, to …
Continuous tensor categories from quantum groups I: algebraic aspects
G Schrader, A Shapiro - arXiv preprint arXiv:1708.08107, 2017 - arxiv.org
We describe the algebraic ingredients of a proof of the conjecture of Frenkel and Ip that the
category of positive representations $\mathcal {P} _\lambda $ of the quantum group $ U_q …
category of positive representations $\mathcal {P} _\lambda $ of the quantum group $ U_q …
Generalized Bäcklund–Darboux transformations for Coxeter–Toda flows from a cluster algebra perspective
M Gekhtman, M Shapiro, A Vainshtein - 2011 - projecteuclid.org
We present the third in the series of papers describing Poisson properties of planar directed
networks in the disk or in the annulus. In this paper we concentrate on special networks N u …
networks in the disk or in the annulus. In this paper we concentrate on special networks N u …
Yang-Baxter maps: dynamical point of view
AP Veselov - Combinatorial Aspect of Integrable Systems, MSJ …, 2007 - projecteuclid.org
A review of some recent results on the dynamical theory of the Yang-Baxter maps (also
known as set-theoretical solutions to thequantum Yang-Baxter equation) is given. The …
known as set-theoretical solutions to thequantum Yang-Baxter equation) is given. The …
Discrete time Toda systems
YB Suris - Journal of Physics A: Mathematical and Theoretical, 2018 - iopscience.iop.org
Discrete time Toda systems - IOPscience Skip to content IOP Science home Accessibility Help
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