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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 {Ei} of… Click to show full abstract
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 {Ei} of T (d, n). This result generalizes the one for the Coxeter group of type Bn 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.
Journal Title: Symmetry
Year Published: 2018
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