Mobius function on cross-section lattices

摘要

Let M be an irreducible algebraic monoid with a reductive unit group G. Then there is an idempotent cross-section Lambda of G x G-orbits that preserves the Zariski closure ordering. The purpose of this paper is to compute the Mobius function on the cross-section lattice Lambda. This is accomplished by analyzing an associated boolean family of face lattices of polytopes and then solving a resulting system of linear equations. (C) 2004 Elsevier Inc. All rights reserved.