On the combinatorics of Kac's asymmetry function

Commentationes mathematicae Universitatis Carolinae

R. M. Green¹ 

关键词: Lie algebra;    Chevalley basis;    heap;   

DOI  :  

学科分类：物理化学和理论化学

来源: Univerzita Karlova v Praze * Matematicko-Fyzikalni Fakulta / Charles University in Prague, Faculty of Mathematics and Physics

【 摘 要 】

We use categories to recast the combinatorial theory of full heaps, which are certain labelled partially ordered sets that we introduced in previous work. This gives rise to a far simpler set of definitions, which we use to outline a combinatorial construction of the so-called loop algebras associated to affine untwisted Kac-Moody algebras. The finite convex subsets of full heaps are equipped with a statistic called parity, and this naturally gives rise to Kac's asymmetry function. The latter is a key ingredient in understanding the (integer) structure constants of simple Lie algebras with respect to certain Chevalley bases, which also arise naturally in the context of heaps.

【 授权许可】

CC BY