This article is cited in 1 paper

Supertraces on the algebras of observables of the rational Calogero models related to the classical root systems

S. E. Konstein

P. N. Lebedev Physical Institute, Russian Academy of Sciences

Abstract: We find a complete set of supertraces on the algebra $H_{W(\mathbf R)}(\nu)$, the algebra of observables of the rational Calogero model with harmonic interaction based on the classical root systems $\mathbf R$ of $B_N$, $C_N$, and $D_N$ types. These results extend the results known for the case $A_{N-1}$. It is shown that $H_{W(\mathbf R)}(\nu)$ admits $q(\mathbf R)$ independent supertraces where $q(B_N)=q(C_N)$ is a number of partitions of $N$ into a sum of positive integers and $q(D_N)$ is a number of partitions of $N$ into a sum of positive integers with even number of even integers.

Received: 04.04.1996

DOI: 10.4213/tmf1005

 English version: Theoretical and Mathematical Physics, 1997, 111:2, 592–600

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