Project

BN-Pairs, Involutions and Ealy-Type Theorems for Generalized Polygons

Code
bof/baf/4y/2024/01/738
Duration
01 January 2024 → 31 December 2025
Funding
Regional and community funding: Special Research Fund
Promotor
Research disciplines
  • Natural sciences
    • Group theory and generalisations
    • Topological groups, Lie groups
    • Geometry
Keywords
Classification Involution Symmetry Generalized polygon BN-pair Moufang conditions
 
Project description

In 1974, Tits published his seminal Springer Lecture Notes in which he classified spherical buildings of rank at least 3, or, equivalently, spherical BN-pairs of rank at least 3. In his book, Tits noted that infinite BN-pairs of rank 2 could not be classified without extra assumptions, and conjectured how the finite BN-pairs of rank 2 would look like. In the meanwhile, this conjecture has been confirmed by several authors, but not without entailing the Classification of Finite Simple Groups (CFSG) — a result which encompasses hundreds of papers totaling tens of thousands of pages.  

Tits had a classification-free proof in mind though — a geometrical proof. 

In this proposal, we will develop new foundations in the theory of generalized polygons (which admit an automorphism group with a BN-pair), so as to solve Tits’s problem as a consequence. We will also consider far-reaching generalizations of Tits’s problem, but do allow the use of CFSG in order to reach the latter goals.