scholarly journals On the length of fully commutative elements

2018 ◽  
Vol 370 (8) ◽  
pp. 5705-5724 ◽  
Author(s):  
Philippe Nadeau
Keyword(s):  
Fully Commutative Elements

scholarly journals Gröbner-Shirshov Bases for Temperley-Lieb Algebras of Complex Reflection Groups

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 438
Author(s):  
Jeong-Yup Lee ◽  
Dong-il Lee ◽  
SungSoon Kim
Keyword(s):  
Reflection Group ◽  
Type B ◽  
Reflection Groups ◽  
Combinatorial Interpretation ◽  
Complex Reflection ◽  
Complex Reflection Groups ◽  
Complex Reflection Group ◽  
Standard Monomials ◽  
Fully Commutative Elements ◽  
The One

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.

scholarly journals On the cyclically fully commutative elements of Coxeter groups

2011 ◽  
Vol 36 (1) ◽  
pp. 123-148 ◽  
Author(s):  
T. Boothby ◽  
J. Burkert ◽  
M. Eichwald ◽  
D. C. Ernst ◽  
R. M. Green ◽  
...  
Keyword(s):  
Coxeter Groups ◽  
Fully Commutative Elements

scholarly journals Fully commutative elements of the complex reflection groups

2020 ◽  
Vol 558 ◽  
pp. 371-394
Author(s):  
Gabriel Feinberg ◽  
Sungsoon Kim ◽  
Kyu-Hwan Lee ◽  
Se-jin Oh
Keyword(s):  
Reflection Groups ◽  
Complex Reflection ◽  
Complex Reflection Groups ◽  
Fully Commutative Elements

scholarly journals Noncrossing partitions, fully commutative elements and bases of the Temperley–Lieb algebra

2016 ◽  
Vol 25 (06) ◽  
pp. 1650035 ◽  
Author(s):  
Thomas Gobet
Keyword(s):  
Bruhat Order ◽  
Base Change ◽  
Noncrossing Partitions ◽  
Fully Commutative Elements ◽  
Change Matrix ◽  
Order Restricted

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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