# Topological quantum field theories from Hecke algebras

Abstract : We construct one-dimensional non-commutative topological quantum field theories (TQFTs), one for each Hecke algebra corresponding to a finite Coxeter system. These TQFTs associate an invariant to each ciliated surface, which is a Laurent polynomial for punctured surfaces. There is a graphical way to compute the invariant using minimal colored graphs. We give explicit formulas in terms of the Schur elements of the Hecke algebra and prove positivity properties for the invariants when the Coxeter group is of classical type, or one of the exceptional types $H_3$, $E_6$ and $E_7$.
Keywords :
Document type :
Preprints, Working Papers, ...

https://hal.archives-ouvertes.fr/hal-03249858
Contributor : Inspire Hep <>
Submitted on : Friday, June 4, 2021 - 12:55:38 PM
Last modification on : Tuesday, June 8, 2021 - 7:56:16 AM

### Citation

Vladimir Fock, Valdo Tatitscheff, Alexander Thomas. Topological quantum field theories from Hecke algebras. 2021. ⟨hal-03249858⟩

Record views