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arXiv · 2008.04173

Lattice of dominant weights of affine Kac-Moody algebras

Krishanu Roy
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Abstract

The dual space of the Cartan subalgebra in a Kac-Moody algebra has a partial ordering defined by the rule that two elements are related if and only if their difference is a non-negative or non-positive integer linear combination of simple roots. In this paper, we study the subposet formed by dominant weights in affine Kac-Moody algebras. We give a more explicit description of the covering relations in this poset. We also study the structure of basic cells in this poset of dominant weights for untwisted affine Kac-Moody algebras of type A.

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Krishanu Roy. 2020-08-10. Lattice of dominant weights of affine Kac-Moody algebras. https://arxiv.org/abs/2008.04173

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