Communications in Number Theory and Physics最新文献_第10页

An odd variant of multiple zeta values 多个zeta值的奇数变体

IF 1.9 3区数学

Communications in Number Theory and Physics Pub Date : 2016-12-15 DOI: 10.4310/cntp.2019.v13.n3.a2

Michael E. Hoffman

引用次数: 64

Intertwining operators and vector-valued modular forms for minimal models 最小模型的交织算子和向量值模形式

IF 1.9 3区数学

Communications in Number Theory and Physics Pub Date : 2016-12-07 DOI: 10.4310/CNTP.2018.V12.N4.A2

Matthew Krauel, Christopher Marks

引用次数: 1

Bounds for smooth Fano weighted complete intersections 光滑Fano加权完全交的界

IF 1.9 3区数学

Communications in Number Theory and Physics Pub Date : 2016-11-29 DOI: 10.4310/CNTP.2020.V14.N3.A3

V. Przyjalkowski, C. Shramov

引用次数: 21

Three Hopf algebras from number theory, physics & topology, and their common background I: operadic & simplicial aspects 来自数论、物理和拓扑学的三个Hopf代数及其共同背景I:操作和简单方面

IF 1.9 3区数学

Communications in Number Theory and Physics Pub Date : 2016-07-01 DOI: 10.4310/cntp.2020.v14.n1.a1

Imma G'alvez-Carrillo, R. Kaufmann, A. Tonks

引用次数: 8

On derived equivalence of general Clifford double mirrors 一般Clifford双镜的导出等价

IF 1.9 3区数学

Communications in Number Theory and Physics Pub Date : 2016-05-15 DOI: 10.4310/cntp.2020.v14.n3.a5

Zhan Li

引用次数: 1

A Yang–Baxter equation for metaplectic ice 元塑性冰的Yang-Baxter方程

IF 1.9 3区数学

Communications in Number Theory and Physics Pub Date : 2016-04-08 DOI: 10.4310/CNTP.2019.V13.N1.A4

Ben Brubaker, Valentin Buciumas, D. Bump

{"title":"A Yang–Baxter equation for metaplectic ice","authors":"Ben Brubaker, Valentin Buciumas, D. Bump","doi":"10.4310/CNTP.2019.V13.N1.A4","DOIUrl":"https://doi.org/10.4310/CNTP.2019.V13.N1.A4","url":null,"abstract":"We will give new applications of quantum groups to the study of spherical Whittaker functions on the metaplectic $n$-fold cover of $GL(r,F)$, where $F$ is a nonarchimedean local field. Earlier Brubaker, Bump, Friedberg, Chinta and Gunnells had shown that these Whittaker functions can be identified with the partition functions of statistical mechanical systems. They postulated that a Yang-Baxter equation underlies the properties of these Whittaker functions. We confirm this, and identify the corresponding Yang-Baxter equation with that of the quantum affine Lie superalgebra $U_{sqrt{v}}(widehat{mathfrak{gl}}(1|n))$, modified by Drinfeld twisting to introduce Gauss sums. (The deformation parameter $v$ is specialized to the inverse of the residue field cardinality.) \u0000For principal series representations of metaplectic groups, the Whittaker models are not unique. The scattering matrix for the standard intertwining operators is vector valued. For a simple reflection, it was computed by Kazhdan and Patterson, who applied it to generalized theta series. We will show that the scattering matrix on the space of Whittaker functions for a simple reflection coincides with the twisted $R$-matrix of the quantum group $U_{sqrt{v}}(widehat{mathfrak{gl}}(n))$. This is a piece of the twisted $R$-matrix for $U_{sqrt{v}}(widehat{mathfrak{gl}}(1|n))$, mentioned above.","PeriodicalId":55616,"journal":{"name":"Communications in Number Theory and Physics","volume":"1 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2016-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70423342","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 50

On the Rankin-Selberg method for higher genus string amplitudes 关于高属弦振幅的Rankin-Selberg方法

IF 1.9 3区数学

Communications in Number Theory and Physics Pub Date : 2016-01-31 DOI: 10.4310/CNTP.2017.v11.n2.a4

I. Florakis, B. Pioline

引用次数: 20

A descendent tropical Landau–Ginzburg potential for $mathbb{P}^2$ $mathbb{P}^2$的派生热带朗多-金兹堡势

IF 1.9 3区数学

Communications in Number Theory and Physics Pub Date : 2016-01-01 DOI: 10.4310/CNTP.2016.V10.N4.A3

Peter Overholser

引用次数: 4

Abstract loop equations, topological recursion and new applications 抽象环方程、拓扑递归及其新应用

IF 1.9 3区数学

Communications in Number Theory and Physics Pub Date : 2015-01-01 DOI: 10.4310/CNTP.2015.V9.N1.A2

G. Borot, B. Eynard, N. Orantin

{"title":"Abstract loop equations, topological recursion and new applications","authors":"G. Borot, B. Eynard, N. Orantin","doi":"10.4310/CNTP.2015.V9.N1.A2","DOIUrl":"https://doi.org/10.4310/CNTP.2015.V9.N1.A2","url":null,"abstract":"loop equations, topological recursion and applications Gaetan Borot, Bertrand Eynard, Nicolas Orantin Abstract We formulate a notion of ”abstract loop equations”, and show that their solution is provided by a topological recursion under some assumptions, in particular the result takes a universal form. The Schwinger-Dyson equation of the one and two hermitian matrix models, and of the Opnq model appear as special cases. We study applications to repulsive particles systems, and explain how our notion of loop equations are related to Virasoro constraints. Then, as a special case, we study in detail applications to enumeration problems in a general class of non-intersecting loop models on the random lattice of all topologies, to SUpNq Chern-Simons invariants of torus knots in the large N expansion. We also mention an application to Liouville theory on surfaces of positive genus.We formulate a notion of ”abstract loop equations”, and show that their solution is provided by a topological recursion under some assumptions, in particular the result takes a universal form. The Schwinger-Dyson equation of the one and two hermitian matrix models, and of the Opnq model appear as special cases. We study applications to repulsive particles systems, and explain how our notion of loop equations are related to Virasoro constraints. Then, as a special case, we study in detail applications to enumeration problems in a general class of non-intersecting loop models on the random lattice of all topologies, to SUpNq Chern-Simons invariants of torus knots in the large N expansion. We also mention an application to Liouville theory on surfaces of positive genus.","PeriodicalId":55616,"journal":{"name":"Communications in Number Theory and Physics","volume":"13 1","pages":"51-187"},"PeriodicalIF":1.9,"publicationDate":"2015-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85411098","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 57

Elliptic genera of Berglund–Hübsch Landau–Ginzburg orbifolds Berglud–Hübsch Landau–Ginzburg轨道褶皱的椭圆属

IF 1.9 3区数学

Communications in Number Theory and Physics Pub Date : 2015-01-01 DOI: 10.4310/CNTP.2015.V9.N4.A4

Minxian Zhu

{"title":"Elliptic genera of Berglund–Hübsch Landau–Ginzburg orbifolds","authors":"Minxian Zhu","doi":"10.4310/CNTP.2015.V9.N4.A4","DOIUrl":"https://doi.org/10.4310/CNTP.2015.V9.N4.A4","url":null,"abstract":"Mirror symmetry was originally formulated as a correspondence between the N = (2, 2) superconformal field theories constructed for a Calabi-Yau n-fold X and for its mirror partner X∨. On the level of cohomology groups, there is a 90-degree rotation of the Hodge diamond, i.e. hp,q(X,C) = hn−p,q(X∨,C). Batyrev’s construction of Calabi-Yau hypersurfaces in Gorenstein Fano toric varieties associated to a pair of reflexive polytopes ([B]) is a prolific source of examples of mirror Calabi-Yau varieties. This construction was later generalized by Borisov to Calabi-Yau complete intersections in Gorenstein Fano toric varieties ([B1]), and further by Batyrev and Borisov to the mirror duality of reflexive Gorenstein cones ([BB1]). They proved that the stringtheoretic Hodge numbers of (singular) Calabi-Yau varieties arising from their constructions satisfy the expected mirror duality ([BB2]). Around the same time, physicists Berglund and Hübsch proposed a way to construct mirror pairs of (2, 2)-superconformal field theories in the formalism of orbifold Landau-Ginzburg theories ([BH]). They considered a nondegenerate invertible polynomial potential W whose transpose W∨ is again a non-degenerate invertible potential. They claimed that there exists a suitable group H such that the Landau-Ginzburg orbifolds W and W∨/H form a mirror pair. Recently, Krawitz found a general construction of the dual group G∨ for any subgroup G of diagonal symmetries of W , and proved an “LG-to-LG” mirror symmetry theorem for the pair (W/G,W∨/G∨) at the level of double-graded state spaces ([K]). Under a certain CY condition, the polynomials W , W∨ define CalabiYau hypersurfacesXW ,XW∨ in (usually different) weighted projective spaces.","PeriodicalId":55616,"journal":{"name":"Communications in Number Theory and Physics","volume":"9 1","pages":"741-761"},"PeriodicalIF":1.9,"publicationDate":"2015-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70423189","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0