This article is an extended version of the minicourse given by the second author at the summer school of the conference Interactions of quantum affine algebras with cluster algebras, current algebras and categorification , held in June 2018 in Washington. The aim of the minicourse, consisting of...
We also state a conjecture for $U_\\varepsilon^{\\mathrm{res}}(L\\mathfrak{sl}_3)$, and we prove it for $l=2$.doi:10.48550/arXiv.1410.2446AnneSophie GleitzmathematicsA.-S. Gleitz, Quantum affine algebras at roots of unity and generalised cluster algebras (2014), arXiv:1410:2446...
Quantum Cluster Algebras and Fusion Products. Q-systems are recursion relations satisfied by the characters of the restrictions of special finite-dimensional modules of quantum affine algebras. They ca... Di,Francesco,Philippe,... - 《Imrn International Mathematics Research Notices》 被引量: 18发表:...
Hernandez, D., Leclerc, B.: Cluster algebras and quantum affine algebras. Duke Math. J. 154(2), 265–341 (2010) Article MathSciNet MATH Google Scholar Lee, K.: On cluster variables of rank two acyclic cluster algebras. To appear in Ann. Comb. Musiker, G., Propp, J.: Combinato...
Middle Lecture Room, Math Building 讲座论坛简介 In this talk, I will give an introduction of the cluster algebras arising from the representation theory of quantum affine algebras. I will construct a common triangular basis of such a cluster algebra, which is parametrized by the tropical points....
$Q$-systems are recursion relations satisfied by the characters of the restrictions of special finite-dimensional modules of quantum affine algebras. They can also be viewed as mutations in certain cluster algebras, which have a natural quantum deformati
Lin and Sturmfels (2009 J. Algebra 322 41... R Kenyon,R Pemantle - 《Journal of Physics A Mathematical & Theoretical》 被引量: 19发表: 2014年 Monoidal categorification and quantum affine algebras II We introduce a new family of real simple modules over the quantum affine algebras, called...
The unrestricted T-system is a family of relations in the Grothen-dieck ring of the category of the finite-dimensional modules of Yangian orquantum affine algebra associated with a complex simple Lie algebra. Theunrestricted T-system admits a reduction called the restricted T-system. Inthis pape...
The classification of affineSU(3) modular invariant partition functions A complete classification of thephysical modular invariant partition functions for the WZNW models is known for very few affine algebras and levels, the mo... T Gannon - 《Communications in Mathematical Physics》 被引量: 203...
We also study their interactions with bases and especially canonically positive bases in affine cluster algebras. 关键词: Cluster algebras Quantized Chebyshev polynomials Principal coefficients Regular components Orthogonal polynomials DOI: 10.1007/s10801-009-0198-8 年份: 2010 ...