Supertraces on the Algebras of Observables of the Rational Calogero Model with Harmonic Potential

We define a complete set of supertraces on the algebra $SH_N(\nu)$, the algebra of observables of the $N$-body rational Calogero model with harmonic interaction. This result extends the previously known results for the simplest cases of $N=1$ and $N=2$ to arbitrary $N$. It is shown that $SH_N(\nu)$ admits $q(N)$ independent supertraces where $q(N)$ is a number of partitions of $N$ into a sum of odd positive integers, so that $q(N)>1$ for $N\ge 3$. Some consequences of the existence of several independent supertraces of $SH_N (\nu )$ are discussed such as the existence of ideals in associated $W_{\infty}$ - type Lie superalgebras.Comment: 22 pages, LATE

Higher Spin Conformal Currents in Minkowski Space

Using unfolded formulation of free equations for massless fields of all spins we obtain explicit form of higher-spin conformal conserved charges bilinear in 4d massless fields of arbitrary spins.Comment: LaTeX, 10 pages. Corrected typo