Stekolshchik, R. (2024). Extraspecial Pairs in the Multiply-Laced Root Systems and Calculating Structure Constants [Preprint]. arXiv:2409.13552v2 [math.RT].
This paper aims to simplify the calculation of structure constants in multiply-laced root systems, specifically those of types Bn, Cn, and F4. The author seeks to reduce the complexity of existing formulas by leveraging the concept of "quartets" and analyzing their properties within each root system.
The author utilizes a theoretical and analytical approach, drawing upon the established framework of root systems, special and extraspecial pairs, and Carter's work on structure constants. The study focuses on classifying "quartets" within Bn, Cn, and F4 root systems based on their properties and deriving simplified formulas for structure constant calculation based on these classifications.
The paper successfully simplifies structure constant calculations for multiply-laced root systems Bn, Cn, and partially for F4. The introduction and analysis of "quartets" provide valuable insights into the structure of these root systems and offer a more efficient approach to calculating structure constants.
This research contributes to the field of Lie algebra and representation theory by providing a more efficient method for calculating structure constants in certain multiply-laced root systems. This simplification can potentially benefit various applications that rely on these calculations, such as those in physics and computer science.
While the study provides a comprehensive analysis of Bn and Cn, the simplification for F4 is limited to a subset of quartets. Further research could explore the remaining quartets in F4 and investigate the applicability of this approach to other multiply-laced root systems, such as G2. Additionally, exploring the computational implications of these simplified formulas and comparing their efficiency to existing methods would be beneficial.
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by Rafael Steko... at arxiv.org 11-04-2024
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