Order of the canonical vector bundle on $C_{n}(K)/\Sigma_{k}$

Abstract

It has been proved that the order of the naturally defined vector bundle on $C_{n}(K)/\Sigma_{k}$, the configuration space of $k$ distinct points in $R^{n}$, is helpful in finding some new elements of maps between spheres. Now, with the help of representation ring, we give some partial results concerning the largest powers of prime numbers dividing the orders.