Möbius function on cross-section lattices

  • Authors:

  • Mohan S. Putcha

  • Affiliations:

  • Department of Mathematics, North Carolina State University, Box 8205, Raleigh, NC

  • Venue:
  • Journal of Combinatorial Theory Series A
  • Year:
  • 2004

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Abstract

Let M be an irreducible algebraic monoid with a reductive unit group G. Then there is an idempotent cross-section Λ of G × G-orbits that preserves the Zariski closure ordering. The purpose of this paper is to compute the Möbius function on the cross-section lattice Λ. This is accomplished by analyzing an associated boolean family of face lattices of polytopes and then solving a resulting system of linear equations.