Uniform cell decomposition with applications to Chevalley groups. (English) Zbl 1275.20053
From the summary: The authors express integrals of definable functions over definable sets uniformly for non-Archimedean local fields, extending results of Pas. They apply this to Chevalley groups, in particular, proving that zeta functions counting conjugacy classes in congruence quotients of such groups depend only on the size of the residue field, for sufficiently large residue characteristic. In particular, the number of conjugacy classes in a congruence quotient depends only on the size of the residue field. The same holds for zeta functions counting dimensions of Hecke modules of intertwining operators associated to induced representations of such quotients.
Reviewer: L. N. Vaserstein (University Park)
MSC:
20G25 | Linear algebraic groups over local fields and their integers |
11M41 | Other Dirichlet series and zeta functions |
22E50 | Representations of Lie and linear algebraic groups over local fields |
03C10 | Quantifier elimination, model completeness, and related topics |