Some progress on locally-primitive generalized polygons

Abstract: Classifications of locally $3$-arc transitive generalized quadrangles and locally $2$-arc transitive generalized quadrangles have been settled in A classification of finite locally 2-transitive generalized quadrangles-Bamberg_Li_Swartz.pdf. A nature question is to consider the classification of locally $2$-arc transitive generalized $n$-gons for $n\in \{6,8\}$, or more generally, the classification of locally primitive generalized $n$-gons for $n\in \{4,6,8\}$. In this talk, we shall give some recent progress on this topic.

Known Examples

Examples of Thick GQs

Classical

这是所有的典型的广义四边形

第一列：polar space 第二列：order $(s,t)$ 这六行：两两典型对偶

Non-classical

Examples of Thick GHs and GOs

Progress on Classifications

GQs

GHs and GOs

Parameter conditions

Remark. Note that $|{\Gamma }_i(x)|$ is the number of points which satisfy $\mathrm{d}(x,p)=i$ for point $p\in \Gamma$.

Main tools

Benson Type Argument

Fixed Element Structure

Normal Quotient Graphs

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Di’s work

并没有仔细听（）

似乎都是用Main tools中的整除关系+parameter conditions？这堆限制也太强了，怪不得广义多边形就那几个（）