Regular representations of affine Kac-Moody algebras
B. Feigin, S. Parkhomenko
TL;DR
This paper explores a Wakimoto-type construction of affine Kac-Moody algebras, resulting in a regular representation where the algebra acts from both sides with levels summing to a specific value related to the dual Coxeter number.
Contribution
It introduces a novel regular representation of affine Kac-Moody algebras with a unique dual-sided action and specific level conditions.
Findings
Constructed a Wakimoto-type regular representation
Demonstrated dual-sided action with levels summing to -2 dual Coxeter numbers
Provides new insights into affine algebra representations
Abstract
In this paper we investigate one Wakimoto-type construction of affine Kac-Moody algebras. We obtain a version of the regular representation, on which the affine algebra acts from the left and from the right with the sum of levels equal to minus two dual Coxeter numbers.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Combinatorial Mathematics · semigroups and automata theory