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Dynkin diagram classification of \(\lambda\)-minuscule Bruhat lattices and of \(d\)-complete posets. (English) Zbl 0920.06003
Summary: \(d\)-complete posets are defined to be posets which satisfy certain local structural conditions. These posets play or conjecturally play several roles in algebraic combinatorics related to the notions of shapes, shifted shapes, plane partitions, and hook length posets. They also play several roles in Lie theory and algebraic geometry related to \(\lambda\)-minuscule elements and Bruhat distributive lattices for simply laced general Weyl or Coxeter groups, and to \(\lambda\)-minuscule Schubert varieties. This paper presents a classification of \(d\)-complete posets which is indexed by Dynkin diagrams.

MSC:
06A07 Combinatorics of partially ordered sets
05E10 Combinatorial aspects of representation theory
17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
20F55 Reflection and Coxeter groups (group-theoretic aspects)
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