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Algebra & Geometry Seminar
Tuesday, September 17, 2024

Time: 3:30 p.m.  Place: Jeffery Hall, Room 422

Speaker: Charles Paquette (RMC & Queen’s University)

Title: Inflations for quotient root systems, and applications to decomposing inversion sets - PART 2

Abstract: This is a report on joint work with I. Dimitrov, C. Gigliotti, E. Ossip and D. Wehlau. In the work of Dewji - Dimitrov - McCabe - Roth - Wehlau - Wilson, the notion of inflation of a permutation of the symmetric group Sn+1 was used to better understand inversion sets and how they yield decompositions of the set of all positive roots of the corresponding root system An. This led to nice geometric applications. A key observation is that inflations for the symmetric group can be defined by combining quotient root systems (QRSs) and subsystems, which are again of type A. In the first part of this talk, after reviewing the case of the symmetric group and type A root systems, we will define inversion sets and inflations for any QRS. Using induction and some new combinatorial objects that we can assign to an inversion set, we explain how to decompose the set of positive roots of a QRS into a disjoint union of inversion sets.