We consider the XXX homogeneous Gaudin system with N sites, both in classical and the quantum case. In particular we show that a suitable limiting procedure for letting the poles of its Lax matrix collide can be used to define new families of Liouville integrals (in the classical case) and new ''Gaudin'' algebras (in the quantum case). We will especially treat the case of total collisions, that gives rise to (a generalization of) the so called Bending flows of Kapovich and Millson. Some aspects of multi-Poisson geometry will be addressed (in the classical case). We will make use of properties of ''Manin matrices'' to provide explicit generators of the Gaudin Algebras in the quantum case

Chervov, A., Falqui, G., & Rybnikov, L. (2009). Limits of Gaudin Systems: Classical and Quantum Cases. SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS, 5, 029 [10.3842/SIGMA.2009.029].

Limits of Gaudin systems: Classical and quantum cases

FALQUI, GREGORIO;
2009

Abstract

We consider the XXX homogeneous Gaudin system with N sites, both in classical and the quantum case. In particular we show that a suitable limiting procedure for letting the poles of its Lax matrix collide can be used to define new families of Liouville integrals (in the classical case) and new ''Gaudin'' algebras (in the quantum case). We will especially treat the case of total collisions, that gives rise to (a generalization of) the so called Bending flows of Kapovich and Millson. Some aspects of multi-Poisson geometry will be addressed (in the classical case). We will make use of properties of ''Manin matrices'' to provide explicit generators of the Gaudin Algebras in the quantum case
Articolo in rivista - Articolo scientifico
Gaudin models, Hamiltonian structures, Gaudin algebras
English
029
Chervov, A., Falqui, G., & Rybnikov, L. (2009). Limits of Gaudin Systems: Classical and Quantum Cases. SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS, 5, 029 [10.3842/SIGMA.2009.029].
Chervov, A; Falqui, G; Rybnikov, L
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10281/6785
Citazioni
  • Scopus 5
  • ???jsp.display-item.citation.isi??? 5
Social impact