Scale Functions on Linear Groups Over Local Skew Fields
✍ Scribed by Helge Glöckner
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 226 KB
- Volume
- 205
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
✦ Synopsis
Let G be a general or special linear group over a local skew field. Then G is a Ž totally disconnected, locally compact group, to which G. Willis Math. Ann. 300, . 1994, 341᎐363 associates its scale function s : G ª .ގ We compute s on the subset of diagonalizable matrices. We also consider the projective situation, and we discuss scale functions on groups of upper triangular matrices. The latter can be computed completely, provided that the underlying field is commutative. The data computed suffice to determine the modular functions on the groups considered, and they facilitate an easy proof of the fact that general or special linear groups over local skew fields with distinct modules cannot be isomorphic as topological groups.