Gröbner-Shirshov Bases for Temperley-Lieb Algebras of Complex Reflection Groups
Keyword(s):
Type B
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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 { 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.
2010 ◽
Vol 147
(3)
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pp. 965-1002
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2011 ◽
Vol DMTCS Proceedings vol. AO,...
(Proceedings)
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2009 ◽
Vol 86
(1)
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pp. 123-138
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2020 ◽
Vol DMTCS Proceedings, 28th...
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