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

By Martina Lanini

Appears in 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.

Information about the video

Date of recording 31/08/2016
Date of publication 13/09/2016
Institution CIRM
Licence CC BY NC ND
Language English
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19042803
Cite this video 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

Domain(s)

Bibliography

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

MSC codes

Document(s)

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

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