  Complete spectrum of exact interdimensional degeneracies for a quantum
$N$-body system in $D$-dimensions is presented by the method of generalized
spherical harmonic polynomials. In an $N$-body system all the states with
angular momentum $[\mu+n]$ in $(D-2n)$ dimensions are degenerate where $[\mu]$
and $D$ are given and $n$ is an arbitrary integer if the representation
$[\mu+n]$ exists for the SO($D-2n$) group and $D-2n\geq N$. There is an
exceptional interdimensional degeneracy for an $N$-body system between the
state with zero angular momentum in $D=N-1$ dimensions and the state with zero
angular momentum in $D=N+1$ dimensions.
