Quantum affine algebras and grassmannians

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August undefined, 2024

WebJul 30, 2024 · PDF We study the relation between quantum affine algebras of type A and Grassmannian cluster algebras. ... {\mathfrak{sl}_n})$-modules to a quotient of the … WebSep 1, 2024 · Introduction. Let g be a simple Lie algebra over C and U q (g ˆ) be the corresponding untwisted quantum affine algebra with quantum parameter q ∈ C × not a root of unity, introduced independently by Drinfeld [11] and Jimbo [23]. Finite-dimensional simple U q (g ˆ)-modules have been classified by Chari and Pressley [7] in terms of Drinfeld …

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WebDec 6, 2024 · This gives a representation-theoretic categorification of the preprojective K-theoretic Hall algebra considered by Schiffmann-Vasserot. Using this categorification, we compare the monoidal categorification of the quantum open unipotent cells of type given by Kang-Kashiwara-Kim-Oh-Park in terms of quiver-Hecke algebras with the one given by ... WebFeb 20, 2006 · Cluster algebras and quantum affine algebras. Duke Mathematical Journal, Vol. 154, Issue. 2, CrossRef; Google Scholar; Grabowski, J. E. and Launois, S. 2010. Quantum Cluster Algebra Structures on Quantum Grassmannians and their Quantum Schubert Cells: The Finite-type Cases. International Mathematics Research Notices, CrossRef; i know a little german

Affine Lie Algebras And Quantum Groups An Introduction With ...

WebAMS Member Price: $68.00. Add to cart. Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version. View Bundle. List Price: WebDec 8, 2024 · We propose a conjectural construction of various slices for double affine Grassmannians as Coulomb branches of 3-dimensional N=4 supersymmetric affine quiver gauge theories. It generalizes the known construction for the usual affine Grassmannian, and makes sense for arbitrary symmetric Kac-Moody algebras. WebOct 1, 2024 · It is a major source of general information about the double affine Hecke algebra, ... six-vertex model with the quantum equivariant cohomology and quantum equivariant K-theory of Grassmannians. is the rolling stone magazine biased

Quantum affine algebras and Grassmannians - Springer

(PDF) Tropical Geometry, Quantum Affine Algebras, and

WebMar 9, 2024 · The goal of this paper is to make a connection between tropical geometry, representations of quantum affine algebras, and scattering amplitudes in physics. The … WebNov 8, 2016 · The main idea, roughly speaking, is to take advantage of the two different descriptions of quantum affine algebras, the Drinfeld--Jimbo and the Kac--Moody realizations. Our main application is to obtain exotic t-structures on certain convolution varieties defined using the Beilinson--Drinfeld and affine Grassmannians. i know a little french in frenchWebMay 23, 2014 · 1. Introduction. Since cluster algebras were introduced by Fomin and Zelevinsky [], it has been recognized that cluster algebra structures on homogeneous coordinate rings on Grassmannians are among the most important classes of examples.The demonstration of the existence of such a structure is due to Scott [] and one reason for … is the rollerworld money real

"WebQuantum affine algebras and Grassmannians 求真书院. Abstract： In this talk, I will talk about the joint work with Wen Chang, Bing Duan, and Chris Fraser on quantum affine algebras of type A and Grassmannian cluster algebras. Let g=sl_k and U_q(^g. Geometry of Discrete Integrable Systems: QRT Maps and Discrete Painlevé Equat... 求真书院 " - Quantum affine algebras and grassmannians

Quantum affine algebras and grassmannians

$arXiv:1304.0323v3 [math.RT] 26 Mar 2024$

WebQuivers play an important role in the representation theory of algebras, with a key ingredient being the path algebra and the preprojective algebra. Quiver grassmannians are varieties of submodules of a fixed module of the path or preprojective algebra. In the current paper, we study these objects in detail. We show that the quiver grassmannians corresponding to … WebJun 22, 2024 · In quantum geometric Langlands, the Satake equivalence plays a less prominent role than in the classical theory. Gaitsgory--Lurie proposed a conjectural substitute, later termed the fundamental local equivalence, relating categories of arc-integrable Kac--Moody representations and Whittaker D-modules on the affine …

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WebMay 23, 2014 · 1. Introduction. Since cluster algebras were introduced by Fomin and Zelevinsky [], it has been recognized that cluster algebra structures on homogeneous … WebJul 31, 2024 · Title: Quantum affine algebras and Grassmannians. Authors: Wen Chang, Bing Duan, Chris Fraser, Jian-Rong Li. Download PDF Abstract: We study the relation between …

WebAug 31, 2024 · In Sect. 3.1, we recall loop Grassmannians and in Sect. 3.2, we check the description of T-fixed points in intersections $ ( \overline {S_0} \cap \overline {S^-_{-{\alpha }}})^T $ of closures of semi-infinite orbits in a loop Grassmannian. This is used in the “homological” reconstruction and generalization of loop Grassmannians in Sect. 3.4, … WebJan 1, 2024 · In two papers [Push-pull operators on the formal affine Demazure algebra and its dual, arXiv:1312.0019] and [A coproduct structure on the formal affine Demazure algebra, arXiv:1209.1676], we ...

http://export.arxiv.org/abs/1907.13575v1 WebFeb 20, 2006 · Cluster algebras and quantum affine algebras. Duke Mathematical Journal, Vol. 154, Issue. 2, CrossRef; Google Scholar; Grabowski, J. E. and Launois, S. 2010. …

WebMay 23, 2014 · We introduce a framework for Z-gradings on cluster algebras (and their quantum analogues) that are compatible with mutation.To do this, one chooses the degrees of the (quantum) cluster variables in an initial seed subject to a compatibility with the initial exchange matrix, and then one extends this to all cluster variables by mutation.

WebFor any simply-laced type simple Lie algebra g and any height function ξ adapted to an orientation Q of the Dynkin diagram of g, Hernandez–Leclerc introduced a certain category C≤ξ of representations of the quantum affine algebra Uq(gˆ), as well as a subcategory CQ of C≤ξ whose complexified Grothendieck ring is isomorphic to the coordinate ring C[N] of a … i know a little bass lessonWebMar 20, 2000 · R. Jaganathan (The Institute of Mathematical Sciences, India) A very elementary introduction to quantum algebras is presented and a few examples of their physical applications are mentioned. Mathematical Physics (math-ph); Condensed Matter (cond-mat); High Energy Physics - Theory (hep-th); Quantum Algebra (math.QA); Nuclear … i know a little guitar chordsWebJan 1, 2024 · In two papers [Push-pull operators on the formal affine Demazure algebra and its dual, arXiv:1312.0019] and [A coproduct structure on the formal affine Demazure … is the rolling stones rockWebn+\ell+1, \sim)]$ of a Grassmannian cluster algebra. We proved that this isomorphism induces an isomorphism $\widetilde{\Phi}$ from the monoid of dominant monomials to the monoid of semi-standard Young tableaux. Using this … i know a little in aslWebFeb 13, 2009 · Quantum affine algebras and Grassmannians. 27 February 2024. Wen Chang, Bing Duan, … Jian-Rong Li. Tropical Grassmannians, cluster algebras and scattering … i know a little chords and lyricshttp://export.arxiv.org/abs/1907.13575v1 i know a little in spanishWebpdf quantum affine algebras and their representations May 20th, 2024 - if uq g is a finite dimensional plex simple lie algebra an affinization of a finite dimensional irreducible representation v of uq g is a finite dimensional irreducible representation v of binatorial interpretations for rank two cluster i know a little german top secret