Sadek Al Harbat

activity

20132025

most citedMarkov trace on a tower of affine Temperley-Lieb algebras of type

A_{n} ~

2 citations · 3 across the 12 of their papers we have counts for

collaborators

12 papers

math.RT2025

Canonical reduced expression in affine Coxeter groups of type $A ~_{n}$ , $B ~_{n}$ , $D ~_{n}$

Sadek Al Harbat

We classify the elements of $W (A ~_{n})$ by giving a canonical reduced expression for each, using basic tools among which affine length. We give some direct consequences for su…

math.CO2023

Catalan numbers: from FC elements to classical diagram algebras

Sadek Al Harbat

Let $W^{c} (A_{n})$ be the set of fully commutative elements in the $A_{n}$ -type Coxeter group. Using only the settings of their canonical form, we recount $W^{c} (A_{n})$ by the recurrence th…

math.RT2021★ 1 cited

Canonical reduced expression for elements of affine Coxeter groups Part I -- Type $A ~_{n}$

Sadek Al Harbat

We classify the elements of $W (A ~_{n})$ by giving a canonical reduced expression for each, using basic tools among which affine length. We give some direct consequences for su…

math.CO2020

Poincaré polynomial for fully commutative elements in the symmetric group

Sadek AL Harbat, Corinne Blondel

Let $W^{c} (A_{n})$ be the set of fully commutative elements of the Coxeter group $W (A_{n})$ . Let $a_{n} (q) = w \in W^{c} (A_{n}) \sum q^{l (w)} .$ We compute $a_{n} (q)$ .

math.CO2019

Type $C ~$ Temperley-Lieb algebra quotients and Catalan combinatorics

Sadek Al Harbat, Camilo González, David Plaza

We study some algebraic and combinatorial features of two algebras that arise as quotients of Temperley-Lieb algebras of type $C ~$ , namely, the two-boundary Temperley-Lieb a…

math.GR2018

On fully commutative elements of type $B ~$ and $D ~$

Sadek AL Harbat

We define a tower of injections of $B ~$ -type (resp. $D ~$ -type) Coxeter groups $W (B ~_{n})$ (resp. $W (D ~_{n})$ ) for $n \geq 3$ . Let $W^{c} (B ~_{n})$ (resp…

math.GR2015

On the fully commutative elements of type $C ~$ and faithfulness of related towers

Sadek Al Harbat

We define a tower of injections of $C ~$ -type Coxeter groups $W (C ~_{n})$ for $n \geq 1$ . We define a tower of Hecke algebras and we use the faithfulness at the Coxeter l…

math.GR2015

Tower of fully commutative elements of type $A ~$ and applications

Sadek Al Harbat

Let $W^{c} (A ~_{n})$ be the set of fully commutative elements in the affine Coxeter group $W (A ~_{n})$ of type $A ~$ . We classify the elements of $W^{c} (A ~_{n})$ …

math.GR2015

A note on affine links

Sadek Al Harbat

We view the $A ~$ -type affine braid group as a subgroup of the $B$ -type braid group. We show that the $A ~$ -type affine braid group surjects onto the $A$ -type braid gro…

math.GR2015

Markov elements in affine Temperley-Lieb algebras

Sadek Al Harbat

We define a tower of affine Temperley-Lieb algebras of type $A_{n} ~$ and we define Markov elements in those algebras. We prove that any trace over an affine Temperley-Lieb a…

math.GR2013

A classification of affine fully commutative elements

Sadek Al Harbat

We classify fully commutative elements in the affine Coxeter group of type $A_{n} ~$ . We give a normal form for such elements, then we propose an application of this normal f…

math.GR2013★ 2 cited

Markov trace on a tower of affine Temperley-Lieb algebras of type $A_{n} ~$

Sadek Al Harbat

We define a tower of affine Temperley-Lieb algebras of type $A_{n} ~$ . We prove that there exists a unique Markov trace on this tower, this trace comes from the Markov-Ocnean…

Canonical reduced expression in affine Coxeter groups of type A~n​, B~n​, D~n​

Catalan numbers: from FC elements to classical diagram algebras

Canonical reduced expression for elements of affine Coxeter groups Part I -- Type A~n​

Poincaré polynomial for fully commutative elements in the symmetric group

Type C~ Temperley-Lieb algebra quotients and Catalan combinatorics

On fully commutative elements of type B~ and D~

On the fully commutative elements of type C~ and faithfulness of related towers

Tower of fully commutative elements of type A~ and applications

A note on affine links

Markov elements in affine Temperley-Lieb algebras

A classification of affine fully commutative elements

Markov trace on a tower of affine Temperley-Lieb algebras of type An​~​

Canonical reduced expression in affine Coxeter groups of type $A ~_{n}$ , $B ~_{n}$ , $D ~_{n}$

Canonical reduced expression for elements of affine Coxeter groups Part I -- Type $A ~_{n}$

Type $C ~$ Temperley-Lieb algebra quotients and Catalan combinatorics

On fully commutative elements of type $B ~$ and $D ~$

On the fully commutative elements of type $C ~$ and faithfulness of related towers

Tower of fully commutative elements of type $A ~$ and applications

Markov trace on a tower of affine Temperley-Lieb algebras of type $A_{n} ~$