Normalizers of compact subgroups, the existence of commuting automorphisms, and applications to operator semistable measures

Abstract: Let $\scriptstyle G$ be a Lie group with finitely many components and $\scriptstyle K$ a compact subgroup with identity component $\scriptstyle K_0$. The normalizer, respectively, centralizer of $\scriptstyle K$ in $\scriptstyle G$ is denoted by $\scriptstyle N(K,G)$, respectively, $\scriptstyle Z(K,G)$. It is shown that $\scriptstyle N(K,G)/K_0Z(K,G)$ is finite. This is applied to a problem in theoretical probability theory, namely, to the characterisation of operator semistable measures. The article explains these concepts and puts the present application into perspective.

Full text of the article:

• Compressed DVI file (44552 Bytes)
• Compressed Postscript file (83425 Bytes)