fully commutative elements
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2022 ◽  
Vol 101 ◽  
pp. 103464
Author(s):  
Eli Bagno ◽  
Riccardo Biagioli ◽  
Frédéric Jouhet ◽  
Yuval Roichman

2020 ◽  
Vol 558 ◽  
pp. 371-394
Author(s):  
Gabriel Feinberg ◽  
Sungsoon Kim ◽  
Kyu-Hwan Lee ◽  
Se-jin Oh

2018 ◽  
Vol 513 ◽  
pp. 466-515 ◽  
Author(s):  
Riccardo Biagioli ◽  
Mireille Bousquet-Mélou ◽  
Frédéric Jouhet ◽  
Philippe Nadeau

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 438
Author(s):  
Jeong-Yup Lee ◽  
Dong-il Lee ◽  
SungSoon Kim

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.


2016 ◽  
Vol 25 (06) ◽  
pp. 1650035 ◽  
Author(s):  
Thomas Gobet

We introduce a new basis of the Temperley–Lieb algebra. It is defined using a bijection between noncrossing partitions and fully commutative elements together with a basis introduced by Zinno, which is obtained by mapping the simple elements of the Birman–Ko–Lee braid monoid to the Temperley–Lieb algebra. The combinatorics of the new basis involve the Bruhat order restricted to noncrossing partitions. As an application we can derive properties of the coefficients of the base change matrix between Zinno’s basis and the well-known diagram or Kazhdan–Lusztig basis of the Temperley–Lieb algebra. In particular, we give closed formulas for some of the coefficients of the expansion of an element of the diagram basis in the Zinno basis.


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