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
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• 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.