On automorphisms of tame polynomial automorphism Ind-Schemes in positive characteristic

In this paper we study certain combinatorial attributes of Ind-schemes of polynomial automorphisms in positive characteristic. In particular, we prove that over an algebraically closed field K of positive characteristic ≠2 every automorphism of the group of origin-preserving automorphisms of the polynomial algebra K[x1,…,xn] (n≥3), which fixes every diagonal matrix, preserves, up to composition with a linear inner automorphism, every tame automorphism.