Gröbner-Shirshov bases for Temperley-Lieb algebras of the complex reflection group of type G(d,1,n)

2018/08/17 by Lee, Jeong-Yup, Lee, Dong-il, Kim, Sungsoon
#05E15 #16Z05 #20F55 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1808.06523

Abstract

We construct a Gröbner-Shirshov basis of the Temperley-Lieb algebra \mathfrakT(d,n) of the complex reflection group G(d,1,n), inducing the standard monomials expressed by the generators \E_i\ of \mathfrakT(d,n). This result generalizes the one for the Coxeter group of type B_n in \citeKimSSLeeDI. We also give a combinatorial interpretation of the standard monomials of \mathfrakT(d,n), relating to the fully commutative elements of the complex reflection group G(d,1,n). In this way, we obtain the dimension formula of \mathfrakT(d,n).

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