Generic patterns for extensions of simple modules for finite Chevalley groups
Let \(G\) be a semi-simple algebraic group over an algebraically closed field \(k\). Denote by \(G(n)\) the finite subgroup of \(G\) consisting of the points over the finite subfield of \(k\) with \(p^n\) elements. In this paper the author compares extensions between simple modules for \(G(n)\) with those of \(G\). (Recall that all simple \(G(n)\)-modules are restrictions of simple \(G\)-modules.) He proves that under certain generic assumptions on the highest weights involved, namely that these are ``deep enough'' inside their alcoves, any such non-trivial extension for \(G\) corresponding to \(n\)-restricted weights is also a non-trivial extension for \(G(n)\). The results extend the author's previous work [J. Algebra 189, No. 1, 101-124 (1997; see the preceding review Zbl 0929.20036)] and may also be considered as a continuation of the reviewer's paper [J. Algebra 111, 388-403 (1987; Zbl 0626.20029)].
scientific article; zbMATH DE number 1271814