Zordan, Michele: Representation zeta functions of special linear groups. 2016
Inhalt
- Introduction
- Chapter 1. Background
- 1.1. p-adic analytic pro-p groups and the Kirillov orbit method
- 1.2. Commutator matrix and Poincaré series
- 1.3. Hensel's lemma
- Chapter 2. Adjoint orbits in Lie rings
- 2.1. Shadows
- 2.2. The action of the kernel
- 2.3. Action of the factor group
- 2.4. Intrinsic description of the orbits
- 2.5. Adjoint orbits
- 2.6. Centralizer and shadow of a lift
- Chapter 3. Special linear groups
- 3.1. Number of lifts
- 3.2. The Poincaré series of sl3(o)
- 3.3. The representation zeta function of SL3m (o)
- Chapter 4. Reduction to the Lie algebra over the finite field
- 4.1. Notation
- 4.2. Poincaré series for Lie rings with smooth and irreducible rank loci
- 4.3. Special linear Groups
- Chapter 5. The representation zeta function of SL4m (o)
- 5.1. Non-degenerate Killing form
- 5.2. Group centralizers in sl4(o)
- 5.3. Centralizers of dimension 3
- 5.4. Centralizers of dimension 5
- 5.5. Centralizers of dimension 7
- 5.6. Centralizers of dimension 9
- 5.7. Poincaré series of sl4(o)
- Bibliography