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 研究仿射李代数表示论及其量子化，包括仿射 Kac-Moody 代数可积表示的协变体理论（与 B. Feigin、M. Jimbo 和 T. Miwa 合作）、量子仿射群的有限维表示理论（与 E. Frenkel 合作）以及李代数表示类别之间的函子 以及由 Knizhnik-Zamolodchikov 和量化 Knizhnik-Zamolodchikov 方程（与 A. Varchenko）定义的量子群。该项目预计将描述与复杂半简单李代数及其仿射和量子类似物的表示论相关的美丽代数组合结构的许多特征。特别是，本研究涉及Young画面的对称函数与组合理论、特殊函数理论、精确可解格模型、共形场论、1+1维质量场论等许多数学领域；因为所有这些理论都具有用不同类型的李代数描述的对称性。