Full metadata record
DC Field | Value | Language |
---|---|---|
dc.contributor.author | 김현규 | - |
dc.date.accessioned | 2020-02-07T16:30:14Z | - |
dc.date.available | 2020-02-07T16:30:14Z | - |
dc.date.issued | 2020 | - |
dc.identifier.issn | 0010-3616 | - |
dc.identifier.issn | 1432-0916 | - |
dc.identifier.other | OAK-26395 | - |
dc.identifier.uri | https://dspace.ewha.ac.kr/handle/2015.oak/253347 | - |
dc.description.abstract | In 2006, Fock and Goncharov constructed a nice basis of the ring of regular functions on the moduli space of framed PGL(2)-local systems on a punctured surface S. The moduli space is birational to a cluster X-variety, whose positive real points recover the enhanced Teichmuller space of S. Their basis is enumerated by integral laminations on S, which are collections of closed curves in S with integer weights. Around ten years later, a quantized version of this basis, still enumerated by integral laminations, was constructed by Allegretti and Kim. For each choice of an ideal triangulation of S, each quantum basis element is a Laurent polynomial in the exponential of quantum shear coordinates for edges of the triangulation, with coefficients being Laurent polynomials in q with integer coefficients. We show that these coefficients are Laurent polynomials in q with positive integer coefficients. Our result was expected in a positivity conjecture for framed protected spin characters in physics and provides a rigorous proof of it, and may also lead to other positivity results, as well as categorification. A key step in our proof is to solve a purely topological and combinatorial ordering problem about an ideal triangulation and a closed curve on S. For this problem we introduce a certain graph on S, which is interesting in its own right. | - |
dc.language | English | - |
dc.publisher | SPRINGER | - |
dc.title | Laurent Positivity of Quantized Canonical Bases for Quantum Cluster Varieties from Surfaces | - |
dc.type | Article | - |
dc.relation.issue | 2 | - |
dc.relation.volume | 373 | - |
dc.relation.index | SCIE | - |
dc.relation.index | SCOPUS | - |
dc.relation.startpage | 655 | - |
dc.relation.lastpage | 705 | - |
dc.relation.journaltitle | COMMUNICATIONS IN MATHEMATICAL PHYSICS | - |
dc.identifier.doi | 10.1007/s00220-019-03411-w | - |
dc.identifier.wosid | WOS:000518629200007 | - |
dc.identifier.scopusid | 2-s2.0-85064333674 | - |
dc.author.google | Cho, So Young | - |
dc.author.google | Kim, Hyuna | - |
dc.author.google | Kim, Hyun Kyu | - |
dc.author.google | Oh, Doeun | - |
dc.contributor.scopusid | 김현규(57020218000) | - |
dc.date.modifydate | 20220901081003 | - |