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Supertraces on the Superalgebra of Observables of Rational Calogero Model based on the Root System

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 Q_R supertraces, where Q_R is the number of conjugacy classes of the Coxeter group G which have no eigenvalue equal to -1.

preprint2012arXivOpen access
S. E. Konstein
math-phmath.MP
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S. E. Konstein

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