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Connection between the ideals generated by traces and by supertraces in the superalgebras of observables of Calogero models
Authors:S.E. Konstein
Affiliation:1. I.E. Tamm Department of Theoretical Physics, P.N. Lebedev Physical Institute, RAS 119991, Leninsky prosp., 53, Moscow, Russiakonstein@lpi.ru
Abstract:If G is a finite Coxeter group, then symplectic reflection algebra H := H1,η (G) has Lie algebra /></span> of inner derivations and can be decomposed under spin: <i>H = H</i><sub>0</sub> ⊕ <i>H</i><sub>1/2</sub> ⊕ <i>H</i><sub>1</sub> ⊕ <i>H</i><sub>3/2</sub> ⊕ …?We show that if the ideals <span class= /></span> of all the vectors from the kernel of degenerate bilinear forms <i>B</i><sub><i>i</i></sub>(<i>x, y</i>) := <i>sp</i><sub><i>i</i></sub> (<i>x · y</i>), where <i>sp</i><sub><i>i</i></sub> are (super)traces on <i>H</i>, do exist, then <span class= /></span> if and only if <span class= /></span>.</td> </tr> <tr> <td align=
Keywords:Intermediate nonlinear Schrödinger equation  integrable systems  Sato theory  nonlocal equation  soliton  bilinear form
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