Branching rule on winding subalgebras of affine Kac-Moody algebras
Khanh Nguyen Duc
TL;DR
This paper develops a branching rule for affine Kac-Moody algebra representations to their winding subalgebras using Lakshmibai-Seshadri paths, providing a combinatorial description of multiplicities and an analog of Steinberg's formula.
Contribution
It introduces a new combinatorial approach to branching rules for affine Kac-Moody algebras via Lakshmibai-Seshadri paths, including a Steinberg-type formula.
Findings
Branching multiplicities described using path combinatorics
Analog of Steinberg's formula established for these multiplicities
Provides explicit combinatorial tools for representation decomposition
Abstract
In this paper, by using the Lakshmibai-Seshadri paths, we give the branching rule for representations of affine Kac-Moody algebras to their winding subalgebras. As a corollary, we can describe branching multiplicities in the language of paths. An analog of Steinberg's formula for branching multiplicities is also given.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Algebraic structures and combinatorial models · Advanced Algebra and Geometry