For Which Pseudo Reflection Groups Are thep-adic Polynomial Invariants Again a Polynomial Algebra?

✍ Scribed by D Notbohm

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 147 KB
• Volume: 214
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1998.7691

✦ Synopsis

Let W be a finite group acting on a lattice L over the p-adic integers ∧ p . The analysis of the ring of invariants of the associated W -action on the algebra ∧ 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 show that W is a pseudo reflection group, if and only if the ring of invariants is again polynomial. We analyze the situation for odd primes dividing the order of W and, in particular, determine those pseudo reflection groups for which the ring of invariants ∧ p L W is a polynomial algebra.