Nahm's equations and root systems
Tomasz Brzezinski, Houari Merabet
TL;DR
This paper presents a novel method for deriving solutions to Nahm's equations using the root structures of simple Lie algebras, linking specific symmetric solutions to particular root systems.
Contribution
It introduces a new approach to solving Nahm's equations by leveraging root systems, exemplified through solutions with tetrahedral and octahedral symmetries.
Findings
Solutions with tetrahedral symmetry correspond to A2 root system
Solutions with octahedral symmetry correspond to A3 root system
The method connects Lie algebra root structures to geometric symmetries in solutions
Abstract
A method of deriving solutions to Nahm's equations based on root structure of simple Lie algebras is given. As an illustration of this method the recently found solutions to Nahm's equations with tetrahedral and octahedral symmetries are shown to correspond to and root systems.
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