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Tutte seminar - Guillauma ChapuyExport this event to calendar

Friday, March 1, 2013 — 3:30 PM to 4:30 PM EST

Counting factorization of Coxeter elements into products of reflections

Speaker: Guillaume Chapuy
Affiliation: LIAFA, France
Room: Mathematics and Computer Building (MC) 5158

Abstract:

A classical formula asserts that the number of factorizations of the full cycle (1,2,...,n) into (n-1) transpositions is n(n-2). I will talk about two generalizations of this result. The first one deals with factorizations of "higher genus", i.e. into (n-1+2g) transpositions for g>0. It is due to Shapiro, Shapiro and Vainshtein in the context of Hurwitz numbers. The second one, where one replaces the symmetric group Sn by any finite subgroup of GLn generated by reflections, and the long cycle by a "Coxeter element" is due to Deligne, and Bessis. I will then present our new result, that generalizes both results simultaneously: we treat the case of "higher genus" factorizations in arbitrary well-generated complex reflection groups (in particular, in finite Coxeter groups).

Joint work with Christian Stump, Hanover.

Location 
MC - Mathematics & Computer Building
5158
200 University Avenue West

Waterloo, ON N2L 3G1
Canada

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