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COADJOINT ORBITS FOR THE CENTRAL EXTENSION OF Diff^+(S^1) AND THEIR REPRESENTATIVES

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Acta Mathematica Scientia 2004年第2期24卷 185-205页

作者：戴佳玲 Doug pickrell Department of Mathematics the University of ArizonaTucsonAZ85721USA

According to Kirillov's idea, the irreducible unitary representations of a Lie group G roughly correspond to the coadjoint orbits (?).In the forward direction one applies the methods of geometric quantization to produce a representation, and in the reverse direction one computes a transform of the character of a representation, to obtain a coadjoint orbit. The method of orbits in the representations of Lie groups suggests the detailed study of coadjoint orbits of a Lie group G in the space (?)~* dual to the Lie algebra (?) of G. In this paper, two primary goals are achieved: one is to completely classify the smooth coadjoint orbits of Virasoro group for nonzero central charge c; the other is to find representatives for coadjoint orbits. These questions have been considered previously by Segal, Kirillov, and witten, but their results are not quite complete. To accomplish this, the authors start by describing the coadjoint action of D-the Lie group of all orientation preserving diffeomorphisms on the circle S^1, and its central extension (?), then the authors will give a complete classification of smooth coadjoint orbits. In fact, they can be parameterized by a subspace Of conjugacy classes of (?)(1,1). Finally, the authors will show how to find representatives f coadjoint orbits by analyzing the vector fields stabilizing the orbits, and describe the amazing connection between the characteristic (trace) of conjugacy classes of (?)(1, 1) and that of vector fields stabilizing orbits.

关键词： Coadjoint representations coadjoint orbits stabilizers vector fields representatives

Seiberg-witten/Whitham Equations and Instanton Corrections in N = 2 Supersymmetric Yang-Mills Theory

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Communications in Theoretical Physics 2018年第5期69卷 558-568页

作者： Jia-Liang Dai En-Gui Fan School of Mathematical Science Fudan University Shanghai 200433 China

We obtain the instanton correction recursion relations for the low energy effective prepotential in pure Ν = 2SU(n) supersymmetric Yang-Mills gauge theory from Whitham hierarchy and Seiberg-witten/Whitham equations. These formulae provide us a powerful tool to calculate arbitrary order instanton corrections coefficients from the perturbative contributions of the effective prepotential in Seiberg-witten gauge theory. We apply this idea to evaluate one-and two-order instanton corrections coefficients explicitly in SU(n) case in detail through the dynamical scale parameter expressed in terms of Riemann's theta-function.

关键词： Whitham hierarchy Seiberg-witten/Whitham equations instanton corrections recursion relations

Ghost Symmetries and Multi-fold Darboux Transformations of Extended Toda Hierarchy

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Chinese Annals of Mathematics,Series B 2020年第5期41卷 697-716页

作者： Chuanzhong LI School of Mathematics and Statistics Ningbo UniversityNingbo 315211ZhejiangChina College of Mathematics and Systems Science Shandong University of Science and TechnologyQingdao 266590ShandongChina

In this paper,the author constructs ghost symmetries of the extended Toda hierarchy with their spectral *** this,two kinds of Darboux transforma-tions in different directions and their mixed Darboux transformations of... 详细信息

关键词： Extended Toda hierarchy Ghost symmetry Spectral representations Hirota quadratic equation Darboux transformation

A COMPACTNESS THEOREM FOR STABLE FLAT SL(2, C) CONNECTIONS ON 3-FOLDS

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Acta Mathematica Scientia 2022年第3期42卷 1160-1172页

作者： Teng HUANG School of Mathematical Sciences University of Science and Technology of China CAS Key Laboratory of Wu Wen-Tsun Mathematics University of Science and Technology of ChinaHefei 230026China

Let Y be a closed 3-manifold such that all flat SU(2)-connections on Y are *** this article,we prove a Uhlenbeck-type compactness theorem on Y for stable flat SL(2,C)connections satisfying an L^(2)-bound for the real *** the compactness theorem and a result from[7],we prove that the moduli space of the stable flat SL(2,C)connections is disconnected under certain technical assumptions.

关键词： Stable flat SL(2,C)connections Vafa-witten equations compactness theorem

Low degree GW invariants of surfaces Ⅱ

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Science China Mathematics 2011年第8期54卷 1679-1706页

作者： KIEM Young-Hoon LI Jun Department of Mathematics and Research Institute of Mathematics Seoul National UniversitySeoul 151-747Korea Department of Mathematics Stanford UniversityStanfordUSA

We prove a conjectural formula of Maulik-Pandharipande on the degree one and two GW invariants of a surface with a smooth canonical *** use the method of degeneration and the localized GW invariants introduced by the ... 详细信息

关键词： Gromov-witten invariant cosection degeneration formula localized virtual cycle

Orbifold Gromov-witten theory of weighted blowups

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Science China Mathematics 2020年第12期63卷 2475-2522页

作者： Bohui Chen Cheng-Yong Du Rui Wang Department of Mathematics and Yangtze Center of Mathematics Sichuan UniversityChengdu 610064China School of Mathematical Sciences and V.C.&V.R.Key Lab Sichuan Normal UniversityChengdu 610068China Department of Mathematics University of CaliforniaBerkeleyBerkeleyCA 94720USA

Consider a compact symplectic sub-orbifold groupoid S of a compact symplectic orbifold groupoid(X,ω).LetXabe the weight-a blowup of X along S,and Da=PNa be the exceptional divisor,where N is the normal bundle of S in *** this paper we show that the absolute orbifold Gromov-witten theory ofXacan be effectively and uniquely reconstructed from the absolute orbifold Gromov-witten theories of X,S and Da,the natural restriction homomorphism HCR^*(X)→HCR*(S)and the first Chern class of the tautological line bundle over *** achieve this we first prove similar results for the relative orbifold Gromov-witten theories of(Xa|Da)and(Na|Da).As applications of these results,we prove an orbifold version of a conjecture of Maulik and Pandharipande(Topology,2006)on the Gromov-witten theory of blowups along complete intersections,a conjecture on the Gromov-witten theory of root constructions and a conjecture on the Leray-Hirsch result for the orbifold Gromov-witten theory of Tseng and You(J Pure Appl Algebra,2016).

关键词： orbifold Gromov-witten theory Leray-Hirsch result weighted projective bundle weighted blowup root stack blowup along complete intersection

Quantum Curve and Bilinear Fermionic Form for the Orbifold Gromov–witten Theory of P[r]

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Acta Mathematica Sinica,English Series 2024年第1期40卷 43-80页

作者： Chong Yao CHEN Shuai GUO Mathematics Department Duke UniversityBox 90320DurhamNC 27708-0320USA School of Mathematical Sciences Peking UniversityBeijing 100871P.R.China

We construct the quantum curve for the Baker-Akhiezer function of the orbifold Gromov-witten theory of the weighted projective line P[r].Furthermore,we deduce the explicit bilinear Fermionic formula for the(stationary... 详细信息

关键词： Quantum curve Free Fermions Gromov-witten invariants Orbifold P^(1)

Ambiguities of the Seiberg-witten Map in the Presence of Matter Field

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Communications in Theoretical Physics 2002年第5期37卷 571-574页

作者： Suo Bing Wang Pei Zhao Liu Institute of Modern Physics Northwest University Xi'an 710069 China

The ambiguities of the Sciberg witten map for gauge field coupled with fermionic matter arc *** find that only part of the ambiguities can be absorbed by gauge transformation and/or field redefinition and thusare negligible. The existence of matter field makes some other part of the ambiguities difficult to be absorbed by gaugetransformation or field redefinition.

关键词：规范场 Sekberg-witten映象物质场

A New Treatment for Some Periodic Schr?dinger Operators Ⅱ: The Wave Function

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Communications in Theoretical Physics 2018年第6期69卷 645-654页

作者： Wei H School of Electronic Engineering Chengdu Technological UniversityChengdu 611730China

Following the approach of our previous paper we continue to study the asymptotic solution of periodic Schrodinger operators. Using the eigenvalues obtained earlier the corresponding asymptotic wave functions are derived. This gives further evidence in favor of the monodromy relations for the Floquet exponent proposed in the previous paper. In particular, the large energy asymptotic wave functions are related to the instanton partition function of N = 2 supersymmetric gauge theory with surface operator. A relevant number theoretic dessert is appended.

关键词： spectral theory periodic differential operators Seiberg-witten duality instanton partition function