Parking spaces and Catalan combinatorics for complex reflection groups | Vidéo | Carmin.tv

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Parking spaces and Catalan combinatorics for complex reflection groups

De Martina Lanini

Apparaît dans la collection : Algebraic Combinatorics in Representation Theory / Combinatoire algébrique en théorie des représentations

Recently, Armstrong, Reiner and Rhoades associated with any (well generated) complex reflection group two parking spaces, and conjectured their isomorphism. This has to be seen as a generalisation of the bijection between non-crossing and non-nesting partitions, both counted by the Catalan numbers. In this talk, I will review the conjecture and discuss a new approach towards its proof, based on the geometry of the discriminant of a complex reflection group. This is an ongoing joint project with Iain Gordon.

Informations sur la vidéo

Date de captation 31/08/2016
Date de publication 13/09/2016
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.19042803
Citer cette vidéo Lanini, Martina (31/08/2016). Parking spaces and Catalan combinatorics for complex reflection groups. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19042803
URL https://dx.doi.org/10.24350/CIRM.V.19042803

Domaine(s)

Bibliographie

D. Armstrong, V. Reiner, B. Rhoades, Parking spaces, Advances in Mathematics 269 (2015), 647-706. - http://arxiv.org/abs/1204.1760
C.A. Athanasiadis, On a refinement of the generalized Catalan numbers for Weyl groups, Trans. Amer. Math. Soc. 357 (2004), 179-196. - http://www.ams.org/journals/tran/2005-357-01/S0002-9947-04-03548-2/home.html
D. Bessis, Finite Complex Reflection Arrangements are K(µ, 1), Annals of Mathematics 181 (2015), 809–904. - http://annals.math.princeton.edu/2015/181-3/p01
P. Biane, Some properties of crossings and partitions, Discrete Math. 175 (1997), 41-53. - http://dx.doi.org/10.1016/S0012-365X(96)00139-2
T. Brady, C. Watt, Non-Crossing Partition Lattices in Finite Real Reflection Groups, Transactions of the AMS 360 (2008), 1983–2005. - http://www.ams.org/journals/tran/2008-360-04/S0002-9947-07-04282-1/S0002-9947-07-04282-1.pdf
V. Ripoll, Lyashko–Looijenga morphisms and submaximal factorizations of a Coxeter element, Journal of Algebraic Combinatorics 36 (2012), 649-673. - http://dx.doi.org/10.1007/s10801-012-0354-4

Codes MSC

Document(s)

http://videos.cirm-math.fr/ressources/ParkingSpacesCIRM2016-2.pdf

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