Powers of the Euler product and commutative subalgebras of a complex simple Lie algebra期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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

Authors:	Email author" target="_blank">Bertram?Kostant Email author

Institution:	(1) Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

Abstract:	If $\mathfrak{g}$ is a complex simple Lie algebra, and k does not exceed the dual Coxeter number of $\mathfrak{g}$ , then the absolute value of the k^th coefficient of the $\dim\mathfrak{g}$ power of the Euler product may be given by the dimension of a subspace of $\wedge^k\mathfrak{g}$ defined by all abelian subalgebras of $\mathfrak{g}$ 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 Petersons 2^rank theorem on the number of abelian ideals in a Borel subalgebra of $\mathfrak{g}$ , an element of type and my heat kernel formulation of Macdonalds -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 $\mathfrak{g}= \text{Lie}\,\mathit{Sl}(m,\mathbb{C})$ ), and the homology and cohomology of the nil radical of the standard maximal parabolic subalgebra of the affine Kac–Moody Lie algebra.

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