Supertraces on the Superalgebra of Observables of Rational Calogero Model based on the Root System
Abstract
The superalgebra of observables of the rational Calogero model based on the root system R is the associative superalgebra generated by polynomials in N indeterminates, the differential-difference Dunkl's operators and the group algebra of the Coxeter group G generated by the root system R. It is shown that this superalgebra possesses QR supertraces, where QR is the number of conjugacy classes of the Coxeter group G which have no eigenvalue equal to -1.
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