Powers of the Euler product and commutative subalgebras of a complex simple Lie algebra

• 成果类型: Article
• 署名作者: Kostant, B
• 署名单位: Massachusetts Institute of Technology (MIT)
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-004-0370-7
• 发表日期: 2004
• 页码: 181-226
• 关键词: cohomology; IDEALS

摘要

If g is a complex simple Lie algebra, and k does not exceed the dual Coxeter number of g, then the absolute value of the k(th) coefficient of the dim g power of the Euler product may be given by the dimension of a subspace of boolean AND(k) g defined by all abelian subalgebras of g of dimension k. This has implications for all the coefficients of all the powers of the Euler product. Involved in the main results are Dale Peterson's 2(rank) theorem on the number of abelian ideals in a Borel subalgebra of g, an element of type rho and my heat kernel formulation of Macdonald's eta-function theorem, a set D-alcove of special highest weights parameterized by all the alcoves in a Weyl chamber (generalizing Young diagrams of null m-core when g=Lie Sl(m, C)), and the homology and cohomology of the nil radical of the standard maximal parabolic subalgebra of the affine Kac-Moody Lie algebra.