Dual approach to Coxeter and Artin-Tits groups

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This project is in the areas finite and infinite group theory and (algebraic) combinatorics, concerning reflection and Coxeter groups, braid and Artin-Tits groups with applications in associative algebras as well as in Hecke algebras and their representations.More precisely, we aim to explore systematically the dual approach in Coxeter and Artin-Tits groups. Our goal is also to apply the dual approach to other areas.The dual Matsumoto property can be used in representation theory of algebras to understand the hereditary k-categories where k is an algebraically closed field.Further, it is conjectured that the extension of the study of Mikado braids to Artin-Tits groups of infinite types yields that the images of the Mikado braids in the Iwahori-Hecke algebra of the respective type have positivity properties: more precisely, when expressing the image of a Mikado braid in the canonical basis of the Hecke algebra. This beside being of interest in its own right, is also of importance in understanding the representation theory of Artin-Tits groups.