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

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Jeong-Yup Lee , Dong-il Lee , Sungsoon Kim ·

YOU? · · 2018 · Open Access · · DOI: https://doi.org/10.3390/sym10100438 · OA: W2892927623

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.