Transactions of the Moscow Mathematical Society最新文献_第6页

Algebraic group actions on normal varieties 正规变种上的代数群作用

Transactions of the Moscow Mathematical Society Pub Date : 2017-03-28 DOI: 10.1090/MOSC/263

M. Brion

引用次数: 19

The dual group of a spherical variety 球面变种的对偶群

Transactions of the Moscow Mathematical Society Pub Date : 2017-02-27 DOI: 10.1090/mosc/270

F. Knop, B. Schalke

引用次数: 15

Examples of lattice-polarized K3 surfaces with automorphic discriminant, and Lorentzian Kac--Moody algebras 具有自同构判别的格极化K3曲面的例子，以及Lorentzian Kac—Moody代数

Transactions of the Moscow Mathematical Society Pub Date : 2017-02-24 DOI: 10.1090/MOSC/265

V. Gritsenko, V. Nikulin

引用次数: 1

Representations of superconformal algebras and mock theta functions 超正则代数和mock theta函数的表示

Transactions of the Moscow Mathematical Society Pub Date : 2017-01-12 DOI: 10.1090/MOSC/268

V. Kac, M. Wakimoto

{"title":"Representations of superconformal algebras and mock theta functions","authors":"V. Kac, M. Wakimoto","doi":"10.1090/MOSC/268","DOIUrl":"https://doi.org/10.1090/MOSC/268","url":null,"abstract":"It is well known that the normaized characters of integrable highest weight modules of given level over an affine Lie algebra $hat{frak{g}}$ span an $SL_2(mathbf{Z})$-invariant space. This result extends to admissible $hat{frak{g}}$-modules, where $frak{g}$ is a simple Lie algebra or $osp_{1|n}$. Applying the quantum Hamiltonian reduction (QHR) to admissible $hat{frak{g}}$-modules when $frak{g} =sl_2$ (resp. $=osp_{1|2}$) one obtains minimal series modules over the Virasoro (resp. $N=1$ superconformal algebras), which form modular invariant families. \u0000Another instance of modular invariance occurs for boundary level admissible modules, including when $frak{g}$ is a basic Lie superalgebra. For example, if $frak{g}=sl_{2|1}$ (resp. $=osp_{3|2}$), we thus obtain modular invariant families of $hat{frak{g}}$-modules, whose QHR produces the minimal series modules for the $N=2$ superconformal algebras (resp. a modular invariant family of $N=3$ superconformal algebra modules). \u0000However, in the case when $frak{g}$ is a basic Lie superalgebra different from a simple Lie algebra or $osp_{1|n}$, modular invariance of normalized supercharacters of admissible $hat{frak{g}}$-modules holds outside of boundary levels only after their modification in the spirit of Zwegers' modification of mock theta functions. Applying the QHR, we obtain families of representations of $N=2,3,4$ and big $N=4$ superconformal algebras, whose modified (super)characters span an $SL_2(mathbf{Z})$-invariant space.","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/MOSC/268","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47514998","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4

Quantum $q$-Langlands Correspondence Quantum$q$-Langlands通信

Transactions of the Moscow Mathematical Society Pub Date : 2017-01-11 DOI: 10.1090/MOSC/278

Mina Aganagic, E. Frenkel, A. Okounkov

引用次数: 88

Matrix divisors on Riemann surfaces and Lax operator algebras Riemann曲面上的矩阵除数与Lax算子代数

Transactions of the Moscow Mathematical Society Pub Date : 2017-01-07 DOI: 10.1090/mosc/267

O. Sheinman

{"title":"Matrix divisors on Riemann surfaces and Lax operator algebras","authors":"O. Sheinman","doi":"10.1090/mosc/267","DOIUrl":"https://doi.org/10.1090/mosc/267","url":null,"abstract":"Matrix divisors are introduced in the work by A.Weil (1938) which is considered as a starting point of the theory of holomorphic vector bundles on Riemann surfaces. In this theory matrix divisors play the role similar to the role of usual divisors in the theory of line bundles. Moreover, they provide explicit coordinates (Tyurin parameters) in an open subset of the moduli space of stable vector bundles. These coordinates turned out to be helpful in integration of soliton equations. \u0000We would like to gain attention to one more relationship between matrix divisors of vector G-bundles (where G is a complex semi-simple Lie group) and the theory of integrable systems, namely to the relationship with Lax operator algebras. The result we obtain can be briefly formulated as follows: the moduli space of matrix divisors with certain discrete invariants and fixed support is a homogeneous space. Its tangent space at the unit is naturally isomorphic to the quotient space of M-operators by L-operators, both spaces essentially defined by the same invariants (the result goes back to Krichever, 2001). We give one more description of the same space in terms of root systems.","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/mosc/267","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45369862","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

Some problems concerning the solvability of the nonlinear stationary Boltzmann equation in the framework of the BGK model 在BGK模型框架下，研究了非线性平稳玻尔兹曼方程的可解性问题

Transactions of the Moscow Mathematical Society Pub Date : 2016-11-28 DOI: 10.1090/MOSC/255

A. Khachatryan, K. Khachatryan

引用次数: 1

The Moscow Mathematical Society and the development of mathematics in Russia (on the 150th anniversary of the Society’s creation) 莫斯科数学学会与俄罗斯数学的发展(纪念该学会成立150周年)

Transactions of the Moscow Mathematical Society Pub Date : 2016-11-28 DOI: 10.1090/MOSC/260

S. Demidov, V. Tikhomirov, T. A. Tokareva

{"title":"The Moscow Mathematical Society and the development of mathematics in Russia (on the 150th anniversary of the Society’s creation)","authors":"S. Demidov, V. Tikhomirov, T. A. Tokareva","doi":"10.1090/MOSC/260","DOIUrl":"https://doi.org/10.1090/MOSC/260","url":null,"abstract":"The Moscow Mathematical Society — the oldest mathematical society in Russia, and one of the oldest in the world — was established one hundred and fifty years ago, in the Autumn of 1864. Its foundation was one of the most significant events in the development of mathematics in Russia, testifying to the creation in the country of a mathematical community that needed special forms of organization for its activities. It should be noted that this was not the first attempt to organize a mathematical society in Moscow: already in 1810, a group of teachers and students at Moscow State University had tried to establish a similar society; see [1, p. 316] and [2]. However, it existed only very briefly: a sufficiently large community of active professional mathematicians had not yet formed in the ancient capital to maintain its regular activities. Until the mid-1830s, Moscow was, in relation to mathematics, profoundly provincial, significantly inferior to St. Petersburg, in which the Imperial Academy of Sciences was located, and Kazan’, workplace of N. I. Lobachevskĭı (see [1]. But by as early as the middle of the nineteenth century, the works of N. D. Brashman and N. E. Zernova of Moscow had become notable points on the mathematical map of Europe.","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2016-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/MOSC/260","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60560485","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Local dynamics of two-component singularly perturbed parabolic systems 双分量奇摄动抛物型系统的局部动力学

Transactions of the Moscow Mathematical Society Pub Date : 2016-11-28 DOI: 10.1090/MOSC/252

I. Kashchenko, S. A. Kashchenko

引用次数: 2

Necessary and sufficient conditions for the topological conjugacy of 3-diffeomorphisms with heteroclinic tangencies 具有异斜切线的3-微分同胚拓扑共轭的充分必要条件

Transactions of the Moscow Mathematical Society Pub Date : 2016-11-28 DOI: 10.1090/MOSC/253

T. M. Mitryakova, O. Pochinka

引用次数: 1