Abelianization of the Cartwright-Steger lattice

G. Blachar, O. Sela–Ben-David, U. Vishne

Abstract


The Cartwright-Steger lattice is a group whose Cayley graph can be identified with the Bruhat-Tits building of \(\operatorname{PGL}_d\) over a local field of positive characteristic. We give a lower bound on the abelianization of this lattice, and report that the bound is tight in all computationally accessible cases.


Keywords


Bruhat-Tits affine building, Cartwright-Steger lattice, abelianization

Full Text:

PDF


DOI: http://dx.doi.org/10.12958/adm1966

Refbacks

  • There are currently no refbacks.