Supertraces on the algebras of observables of the rational Calogero models related to the classical root systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 111 (1997) no. 2, pp. 252-262
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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.
@article{TMF_1997_111_2_a6,
author = {S. E. Konstein},
title = {Supertraces on the algebras of observables of the rational {Calogero} models related to the classical root systems},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {252--262},
publisher = {mathdoc},
volume = {111},
number = {2},
year = {1997},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1997_111_2_a6/}
}
TY - JOUR AU - S. E. Konstein TI - Supertraces on the algebras of observables of the rational Calogero models related to the classical root systems JO - Teoretičeskaâ i matematičeskaâ fizika PY - 1997 SP - 252 EP - 262 VL - 111 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_1997_111_2_a6/ LA - ru ID - TMF_1997_111_2_a6 ER -
%0 Journal Article %A S. E. Konstein %T Supertraces on the algebras of observables of the rational Calogero models related to the classical root systems %J Teoretičeskaâ i matematičeskaâ fizika %D 1997 %P 252-262 %V 111 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_1997_111_2_a6/ %G ru %F TMF_1997_111_2_a6
S. E. Konstein. Supertraces on the algebras of observables of the rational Calogero models related to the classical root systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 111 (1997) no. 2, pp. 252-262. http://geodesic.mathdoc.fr/item/TMF_1997_111_2_a6/