Representations of Infinite-dimensional Lie Algebras

无限维李代数的表示

• 批准号: 0140460
• 负责人: Evgeny Mukhin
• 金额: $ 6.49万
• 依托单位: Indiana University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-06-01 至 2005-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0140460&HistoricalAwards=false
• 关键词: Representations; Infinite; dimensional; Lie; Algebras

AbstractMukhinE. Mukhin studies the representation theory of affine Liealgebras and their quantizations in several directions including thetheory of coinvariants of integrable representations of affineKac-Moody algebras (with B. Feigin, M. Jimbo and T. Miwa), the theoryof finite-dimensional representations of quantum affine groups (withE. Frenkel) and the functors between categories of representations ofLie algebras and quantum groups defined by Knizhnik-Zamolodchikov andquantized Knizhnik-Zamolodchikov equations (with A. Varchenko). The project is expected to result in description of many features ofthe beautiful algebraic-combinatorial structure related torepresentation theory of complex semi-simple Lie algebras and their affine andquantum analogs. In particular, this research has connections to many areas ofmathematics such as theory of symmetric functions and combinatorics ofYoung tableaux, theory of special functions, exactly solvable latticemodels, conformal field theory, massive field theory in 1+1dimensions, etc; as all these theories have symmetries described interms of Lie algebras of different kind.

摘要mukhine。 Mukhin研究了仿生肠道的代表理论及其在多个方向上进行的量化理论，包括共同表示的共同表示，仿生的代数（与B. feigin，M。Jimbo和T. Miwa），量子仿生组的有限分类和firneke firse。和量子组由Knizhnik-Zamolodchikov定义，并量化的Knizhnik-Zamolodchikov方程（带有A. varchenko）。预计该项目将导致描述美丽的代数 - 组合结构相关的复杂半简单谎言代数及其仿射和Quantum类似物的许多特征。特别是，这项研究与许多数学领域的联系，例如对称函数理论和young tableaux的组合，特殊功能理论，准确的可解决的latticeModels，保形田地理论，1+1 iMensions中的大规模领域理论，等等；由于所有这些理论都具有对称性，描述了不同类型的谎言代数的Interms。