LATTICE OF DOMINANT WEIGHTS OF AFFINE KAC-MOODY ALGEBRAS

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 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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https://hal.archives-ouvertes.fr/hal-02331491
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Submitted on : Thursday, October 24, 2019 - 1:43:57 PM
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Krishanu Roy. LATTICE OF DOMINANT WEIGHTS OF AFFINE KAC-MOODY ALGEBRAS. 2019. ⟨hal-02331491⟩

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