Abstract
In this talk we introduce generalised Calogero–Moser models and demonstrate their integrability by constructing universal Lax pair operators. These include models based on non-crystallographic root systems, that is the root systems ofthe finite reflection groups, H3, H4, and the dihedral group I2(m), besides the well-known ones based on crystallographic root systems, namely those associated with Lie algebras. Universal Lax pair operators for all of the generalised Calogero–Moser models and for any choices ofthe potentials are linear combinations ofthe reflection operators. The equivalence ofthe Lax pair with the equations ofmotion is proved by decomposing the root system into a sum oftwo-dimensional sub-root systems, A2, B2, G2 ,a ndI2(m). The root type and the minimal type Lax pairs, derived in our previous papers, are given as the simplest representations. The spectral parameter dependence plays an important role in the Lax pair operators, which bear a strong resemblance to the Dunkl operators.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
