Fully commutative elements in finite and affine Coxeter groups

Autor: Riccardo Biagioli, Philippe Nadeau, Frédéric Jouhet
Přispěvatelé: Combinatoire, théorie des nombres (CTN), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS), Biagioli R, Frédéric Jouhet, Philippe Nadeau
Jazyk: angličtina
Rok vydání: 2015
Předmět:
algèbres de Temperley-Lieb
General Mathematics
éléments pleinement commutatifs
05E15
05A15
0102 computer and information sciences
Point group
01 natural sciences
Fully commutative element
chemins
Combinatorics
Temperley-Lieb algebra
[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
FOS: Mathematics
Mathematics - Combinatorics
empilements de pièces
0101 mathematics
Longest element of a Coxeter group
Mathematics::Representation Theory
Commutative property
Mathematics
Generating function
Groupes de Coxeter
Mathematics::Combinatorics
Coxeter notation
Lattice walk
010102 general mathematics
Coxeter group
[MATH.MATH-RA]Mathematics [math]/Rings and Algebras [math.RA]
fonctions génératrices
Mathematics - Rings and Algebras
Heaps
Rings and Algebras (math.RA)
010201 computation theory & mathematics
Coxeter complex
Artin group
05E15
05A15
Combinatorics (math.CO)
Coxeter element
Zdroj: Monatshefte für Mathematik
Monatshefte für Mathematik, Springer Verlag, 2015, 178 (1), pp.1-37. ⟨10.1007/s00605-014-0674-7⟩
ISSN: 0026-9255
1436-5081
DOI: 10.1007/s00605-014-0674-7⟩
Popis: An element of a Coxeter group $W$ is fully commutative if any two of its reduced decompositions are related by a series of transpositions of adjacent commuting generators. These elements were extensively studied by Stembridge, in particular in the finite case. They index naturally a basis of the generalized Temperley--Lieb algebra. In this work we deal with any finite or affine Coxeter group $W$, and we give explicit descriptions of fully commutative elements. Using our characterizations we then enumerate these elements according to their Coxeter length, and find in particular that the corrresponding growth sequence is ultimately periodic in each type. When the sequence is infinite, this implies that the associated Temperley--Lieb algebra has linear growth.
37 pages, 27 figures
Databáze: OpenAIRE
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