Sortable elements and Cambrian lattices

• Autores: Nathan Reading
• Localización: Algebra universalis, ISSN 0002-5240, Vol. 56, Nº. 3-4, 2007, págs. 411-437
• Idioma: inglés
• DOI: 10.1007/s00012-007-2009-1
• Texto completo no disponible (Saber más ...)
• Resumen

  • We show that the Coxeter-sortable elements in a finite Coxeter group W are the minimal congruence-class representatives of a lattice congruence of the weak order on W. We identify this congruence as the Cambrian congruence on W, so that the Cambrian lattice is the weak order on Coxeter-sortable elements. These results exhibit W-Catalan combinatorics arising in the context of the lattice theory of the weak order on W.