Many-body integrable systems implied by WLZZ models. (English) Zbl 1523.81222
Summary: We provide some details about the recently discovered integrable systems implied by commutativity of \(W\) operators along the rays on the plane of roots of \(w_\infty \)-algebra. The simplest system of this type is the rational Calogero model, other systems escaped attention in the past. Existence of these systems is intimately tied to the very interesting WLZZ matrix models, which are now under intensive study.
MSC:
| 81V70 | Many-body theory; quantum Hall effect |
| 81R12 | Groups and algebras in quantum theory and relations with integrable systems |
| 33D67 | Basic hypergeometric functions associated with root systems |
| 81T32 | Matrix models and tensor models for quantum field theory |
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