ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

7. Lie Groups and Lie Algebras

1991 MS Classification: 22E20 (main), 20G25, 22D05 Glöckner, Helge, TU Darmstadt, Germany Scale functions on p-adic Lie groups Let G be a p-adic Lie group. Then G is a locally compact, totally disconnected group, to which [1] associates its scale function s_{G}: G → ℕ. We show that s_{G} can be computed on the Lie algebra level. The image of s_{G} consists of powers of p. If G is a linear algebraic group over ℚ_{p}, s_{G}(x) = s_{G}(x_{s}) is determined by the semisimple part x_{s} of x ∈ G. For every finite extension K/ℚ_{p}, the scale functions on G and H := G(K) are related by s_{H}|_{G} = s_{G}^{[K:ℚ_{p}]}. References: 1. G. Willis, The structure of locally compact, totally disconnected groups, Math. Ann. 300 (1994), 341–363.

2. H. Glöckner, Scale functions on p-adic Lie groups, to appear.