QUANTUM
   INTEGRABLE
   SYSTEMS and
   GEOMETRY
   2012









 3-7 SEPTEMBER 2012
 OLHÃO, PORTUGAL

Dynamical reflection algebras: examples from Calogero-Moser models

Jean Avan

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A major feature of quantum integrable systems is the quantum group structure encapsulated in the Yang Baxter equation RTT = TTR. The presence of boundaries to a quantum integrable system imposes to complement it by the boundary equation RKRK = KRKR. In parallel consistent deformations of the YB algebra have been defined, leading to so-called dynamical Yang Baxter equations. The work presented here aims at exploring the association of both generalizations as dynamical boundary algebras. Three such structures are known at this time. We will describe these algebraic structures and unravel their connections with the famous integrable N-body Calogero-Moser model, focusing on the rational potential case v(r) = 1/r.