Graphical Calculus for the Double Affine Q-Dependent Braid Group - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year :

## Graphical Calculus for the Double Affine Q-Dependent Braid Group

Glen Burella
• Function : Author
Paul Watts
Vincent Pasquier
• Function : Author
Jiri Vala
• Function : Author

#### Abstract

We define a double affine $Q$-dependent braid group. This group is constructed by appending to the braid group a set of operators $Q_i$, before extending it to an affine $Q$-dependent braid group. We show specifically that the elliptic braid group and the double affine Hecke algebra (DAHA) can be obtained as quotient groups. Complementing this we present a pictorial representation of the double affine $Q$-dependent braid group based on ribbons living in a toroid. We show that in this pictorial representation we can fully describe any DAHA. Specifically, we graphically describe the parameter $q$ upon which this algebra is dependent and show that in this particular representation $q$ corresponds to a twist in the ribbon.

### Dates and versions

cea-01059518 , version 1 (01-09-2014)

### Identifiers

• HAL Id : cea-01059518 , version 1
• ARXIV :

### Cite

Glen Burella, Paul Watts, Vincent Pasquier, Jiri Vala. Graphical Calculus for the Double Affine Q-Dependent Braid Group. 2013. ⟨cea-01059518⟩

### Export

BibTeX TEI Dublin Core DC Terms EndNote Datacite

191 View