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I saw the following results on affine Bruhat-Tits building associated to $\mathrm{SU}_3(\mathbb Q_p)$ without giving any references, where $\mathrm{SU}_3$ is the quasi-split inner form of special unitary group in three variables, with respect to some quadratic extension $E/\mathbb Q_p$:

The tree is homogeneous of degree $q +1$ when $E$ is a ramified extension of $\mathbb Q_p$. It is bihomogeneous when $E$ is an unramified extension of $\mathbb Q_p$, and there exists set $A_1, A_2$ of vertices such that each $v \in A_1$ has $q^3+1$ neighbours and each $v\in A_2$ has $q+1$ neighbours.

Is there any references on that?

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    $\begingroup$ "There are many results": you probably need to be more specific to obtain a useful answer. $\endgroup$
    – YCor
    Commented Jun 10, 2022 at 15:35
  • $\begingroup$ One possible reference is Tits' Corvallis article, Sections 1.15 and 2.7. $\endgroup$
    – krl
    Commented Jul 31, 2022 at 5:20

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A reference for the result you are interested in is :

Choucroun, F. M. (1996). Sous-groupes discrets des groupes p-adiques de rang un et arbres de Bruhat-Tits. Israel Journal of Mathematics, 93, 195-219.

His Theorems 14 and 15 give what you want.

Choucroun mainly uses the decription of the buildings of classical groups given in Bruhat and Tits's article :

[B-T 1 & 2] F. Bruhat et J. Tits,Schémas en groupes et immeubles des groupes classiques sur un corps local, 1re partie: le groupe linéaire général, Bulletin de la Société Mathématique de France112 (1984), 259–301; 2e partie: groupes unitaires Bulletin de la Société Mathématique de France115 (1987), 141–195.

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