5 citations · 13 across the 10 of their papers we have counts for
11 papers
Applications of the Fixed Point Theorem for group actions on buildings to algebraic groups over polynomial rings
Peter Abramenko, Andrei S. Rapinchuk, Igor A. Rapinchuk
We apply the Fixed Point Theorem for the actions of finite groups on Bruhat-Tits buildings and their products to establish two results concerning the groups of points of reductive…
Finite presentability of Kac-Moody groups over finite fields
Peter Abramenko, Zachary Gates
Let be a Kac-Moody group functor in the sense of Tits, with associated Coxeter system . For any field , the group is finitely generated iff…
Distance regularity in buildings and structure constants in Hecke algebras
Peter Abramenko, James Parkinson, Hendrik Van Maldeghem
In this paper we define generalised spheres in buildings using the simplicial structure and Weyl distance in the building, and we derive an explicit formula for the cardinality of…
A classification of commutative parabolic Hecke algebras
Peter Abramenko, James Parkinson, Hendrik Van Maldeghem
Let be a Coxeter system with such that the parabolic subgroup is finite. Associated to this data there is a \textit{Hecke algebra} $\scH$ and a \textit…
Some reductive anisotropic groups that admit no non-trivial split spherical BN-pairs
Peter Abramenko, Matthew C. B. Zaremsky
We prove, for any infinite field k, that any virtually trivial split spherical BN-pair in the group G(k) of k-rational points of a reductive k-group G is already trivial. We then i…
Strongly and Weyl transitive group actions on buildings arising from Chevalley groups
Peter Abramenko, Matthew C. B. Zaremsky
Let K be a field and g(K) a Chevalley group (scheme) over K. Let (B,N) be the standard spherical BN-pair in g(K), with T=B\cap N and Weyl group W=N/T. We prove that there exist non…