Teoretičeskaâ i matematičeskaâ fizika, Tome 111 (1997) no. 2, pp. 252-262
Citer cet article
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/
@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},
year = {1997},
volume = {111},
number = {2},
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
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
%U http://geodesic.mathdoc.fr/item/TMF_1997_111_2_a6/
%G ru
%F TMF_1997_111_2_a6
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.
