Abstract
A root system is splint if it is a decomposition into a union of two disjoint root systems. Examples of such root systems arise naturally in studying embeddings of reductive Lie subalgebras into simple Lie algebras. Given a splint root system, one can try to understand its branching rule. In this paper we discuss methods to understand such branching rules, and give precise formulas for specific cases, including the restriction functor from the exceptional Lie algebra \(\mathfrak {g}_{2}\) to \(\mathfrak {sl}_{3}\).
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Presented by: Vyjayanthi Chari
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Crew, L., Kirillov, A.A. & Yeo, YR. Branching Rules for Splint Root Systems. Algebr Represent Theor 25, 963–981 (2022). https://doi.org/10.1007/s10468-021-10055-9
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DOI: https://doi.org/10.1007/s10468-021-10055-9
Keywords
- Branching rules
- Splint root systems
- Restricted representations
- Lie algebras
- Weyl character formula
- Littlewood-Richardson rule