Dynkin Diagram Classification of λ-Minuscule Bruhat Latticesand of d-Complete Posets

Authors:
Robert A. Proctor
Affiliations:
Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599. rap@math.unc.edu
Venue:
Journal of Algebraic Combinatorics: An International Journal
Year:
1999

Citing 4
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Abstract

d-Complete posets are defined to be posets which satisfycertain local structural conditions. These posets play or conjecturallyplay several roles in algebraic combinatorics related to the notions ofshapes, shifted shapes, plane partitions, and hook length posets. Theyalso play several roles in Lie theory and algebraic geometry related to λ-minuscule elements and Bruhat distributive lattices for simply lacedgeneral Weyl or Coxeter groups, and to λ-minuscule Schubert varieties. This paper presents a classification of d-complete posets which is indexed by Dynkin diagrams.