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Article Dans Une Revue Symmetry Année : 2018

Gröbner-Shirshov Bases for Temperley-Lieb Algebras of Complex Reflection Groups

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Jeong-Yup Lee
  • Fonction : Auteur
Dong-Il Lee

Résumé

We construct a Gröbner-Shirshov basis of the Temperley-Lieb algebra T ( d , n ) of the complex reflection group G ( d , 1 , n ) , inducing the standard monomials expressed by the generators { E i } of T ( d , n ) . This result generalizes the one for the Coxeter group of type B n in the paper by Kim and Lee We also give a combinatorial interpretation of the standard monomials of T ( d , n ) , relating to the fully commutative elements of the complex reflection group G ( d , 1 , n ) . More generally, the Temperley-Lieb algebra T ( d , r , n ) of the complex reflection group G ( d , r , n ) is defined and its dimension is computed.

Dates et versions

hal-03882175 , version 1 (02-12-2022)

Identifiants

Citer

Jeong-Yup Lee, Dong-Il Lee, Sungsoon Kim. Gröbner-Shirshov Bases for Temperley-Lieb Algebras of Complex Reflection Groups. Symmetry, 2018, 10 (10), pp.438. ⟨10.3390/sym10100438⟩. ⟨hal-03882175⟩
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