On decomposition of modular representations from Cohen-Macaulay geometries

Abstract

Chain spaces for a Cohen-Macaulay complex split into subspaces corresponding to cycles for truncations of the complex precisely when the cycles are non-degenerate in the natural bilinear form. Application to the Tits building provides a simple geometric approach to the well known splitting of IndGB(1) for a Lie-type group G in natural characteristic. An application to a "sporadic geometry" is also indicated. © 1990.