New Unifying Structures in Lie Theory and the Cubic Dirac Operator

李理论和三次狄拉克算子的新统一结构

基本信息

  • 批准号:
    0209473
  • 负责人:
  • 金额:
    $ 12.35万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Continuing Grant
  • 财政年份:
    2002
  • 资助国家:
    美国
  • 起止时间:
    2002-06-15 至 2007-05-31
  • 项目状态:
    已结题

项目摘要

A whole array of questions in different mathematical areas seemto be converge to questions having to do with the set of alcovesin a fixed Weyl chamber of a semisimple Lie group. The areasinclude Kac-Moody theory, homology of loop groups, quantumcohomology, the Verlinde algebra, MacDonald identities, Schubertcalculus, ideals in the Borel subalgebra, symmetric space theoryand the Cartan-Weyl representation theory of compact Liegroups. In effect our proposal is to sort out what is going on tounify what seems to us to be unifiable in the subjects listedabove.Group theory, and especially Lie group theory, lies at the heartof mathematics and the application of mathematics to problems inthe real world. Included in the latter are applications to bothclassical and quantum mechanics, control theory, string theory,chemistry and crystallography. Lie group theory is extremelyintricate and the extent to which it is applicable depends highlyon a knowledge of its intricacies. The proposed project expectsto discover highly exciting new structures in the subject andwould unify many existing structures. The effect that would be togreatly increase our understanding and our ability to use thesepowerful structures. This award is jointly funded by the programsin Geometric Analysis and Algebra, Number Theory, & Combinatorics.
在不同的数学领域中的一系列问题都可能收敛到与半单李群的固定外尔腔中的凹室集合有关的问题。这些领域包括Kac-Moody理论、圈群的同调、量子上同调、Verlinde代数、MacDonald恒等式、Schubert演算、Borel子代数中的理想、对称空间理论和紧李群的Cartan-Weyl表示理论。实际上,我们的建议是整理出正在发生的事情,统一在上面提到的学科中我们似乎可以统一的东西。群论,特别是李群理论,是数学的核心,也是数学在真实的世界中应用问题的核心。包括在后者是应用bothclassical和量子力学,控制理论,弦理论,化学和晶体学。李群理论是非常复杂的,它的适用范围在很大程度上取决于对它的复杂性的了解。该项目预计将在该主题中发现非常令人兴奋的新结构,并将统一许多现有的结构。这将极大地增加我们的理解和使用这些强大结构的能力。 该奖项由几何分析和代数,数论,组合数学项目共同资助。

项目成果

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Bertram Kostant其他文献

On some exotic finite subgroups of E 8 and Springer’s regular elements of the Weyl group
  • DOI:
    10.1007/s00031-010-9099-0
  • 发表时间:
    2010-06-08
  • 期刊:
  • 影响因子:
    0.400
  • 作者:
    Bertram Kostant
  • 通讯作者:
    Bertram Kostant
Structure of the truncated icosahedron (e.g. fullerene or C60, viral coatings) and a 60-element conjugacy class inPSl(2, 11)
  • DOI:
    10.1007/bf01614076
  • 发表时间:
    1995-03-01
  • 期刊:
  • 影响因子:
    1.200
  • 作者:
    Bertram Kostant
  • 通讯作者:
    Bertram Kostant

Bertram Kostant的其他文献

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{{ truncateString('Bertram Kostant', 18)}}的其他基金

Mathematical Sciences: Group Theory and Differential Geometry
数学科学:群论和微分几何
  • 批准号:
    9625941
  • 财政年份:
    1996
  • 资助金额:
    $ 12.35万
  • 项目类别:
    Continuing Grant
Mathematical Sciences: Representation Theory and Differential Geometry
数学科学:表示论和微分几何
  • 批准号:
    9307460
  • 财政年份:
    1993
  • 资助金额:
    $ 12.35万
  • 项目类别:
    Continuing Grant
Mathematical Sciences: Representation Theory and Differential Geometry
数学科学:表示论和微分几何
  • 批准号:
    9009450
  • 财政年份:
    1990
  • 资助金额:
    $ 12.35万
  • 项目类别:
    Continuing grant
Mathematical Sciences: Representation Theory and Differential Geometry
数学科学:表示论和微分几何
  • 批准号:
    8703278
  • 财政年份:
    1987
  • 资助金额:
    $ 12.35万
  • 项目类别:
    Continuing grant
Mathematical Sciences: Representation Theory and Differential Geometry
数学科学:表示论和微分几何
  • 批准号:
    8403203
  • 财政年份:
    1984
  • 资助金额:
    $ 12.35万
  • 项目类别:
    Continuing Grant
Representation Theory and Differential Geometry
表示论与微分几何
  • 批准号:
    8105633
  • 财政年份:
    1981
  • 资助金额:
    $ 12.35万
  • 项目类别:
    Continuing grant
Representation Theory and Differential Geometry
表示论与微分几何
  • 批准号:
    7804007
  • 财政年份:
    1978
  • 资助金额:
    $ 12.35万
  • 项目类别:
    Continuing Grant
Representation Theory and Differential Geometry
表示论与微分几何
  • 批准号:
    7609177
  • 财政年份:
    1976
  • 资助金额:
    $ 12.35万
  • 项目类别:
    Standard Grant
Representation Theory and Topology and Number Theory
表示论与拓扑和数论
  • 批准号:
    7102936
  • 财政年份:
    1971
  • 资助金额:
    $ 12.35万
  • 项目类别:
    Standard Grant

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