For which pseudo reflection groups are the p-adic polynomial invariants again a polynomial algebra?

Let W be a finite group acting on a lattice L over the p-adic integers Z(p) <^>. The analysis of the ring of invariants of the associated W-action on t he algebra Z(p)<^>[L] of polynomial functions on L is a classical question of invariant theory. If p is coprime to the order of W, classical results s how that W is a pseudo reflection group, if and only if the ring of invaria nts is again polynomial. We analyze the situation for odd primes dividing t he order of W and, in particular, determine those pseudo reflection groups for which the ring of invariants Z(p)<^>[L](W) is a polynomial algebra. (C) 1999 Academic Press.