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Parking spaces and Catalan combinatorics for complex reflection groups
Post-edited
Authors : Lanini, Martina (Author of the conference)
CIRM (Publisher )
05A19 - Combinatorial identities, bijective combinatorics
06B15 - Representation theory
55R80 - Discriminantal varieties - Configuration spaces
Additional resources :
http://videos.cirm-math.fr/ressources/ParkingSpacesCIRM2016-2.pdf
CIRM (Publisher )
Abstract :
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.
MSC Codes : 05A19 - Combinatorial identities, bijective combinatorics
06B15 - Representation theory
55R80 - Discriminantal varieties - Configuration spaces
Additional resources :
http://videos.cirm-math.fr/ressources/ParkingSpacesCIRM2016-2.pdf
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 13/09/2016 Conference Date : 31/08/2016 Subseries : Research talks arXiv category : Combinatorics ; Algebraic Geometry ; Representation Theory Mathematical Area(s) : Algebra ; Geometry ; Number Theory Format : MP4 (.mp4) - HD Video Time : 01:09:03 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2016-08-31_Lanini.mp4 
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Information on the Event
Event Title : Algebraic Combinatorics in Representation Theory / Combinatoire algébrique en théorie des représentationsEvent Organizers : Beck, Vincent ; Hernandez, David ; Jacon, Nicolas ; Littelmann, Peter Dates : 29/08/2016 - 02/09/2016 Event Year : 2016 Event URL : http://conferences.cirm-math.fr/1490.html
Citation Data
DOI : 10.24350/CIRM.V.19042803Cite this video as: Lanini, Martina (2016). Parking spaces and Catalan combinatorics for complex reflection groups. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19042803 URI : http://dx.doi.org/10.24350/CIRM.V.19042803 |
See Also
- [Multi angle] Studying affine Deligne Lusztig varieties via folded galleries in buildings / Author of the conference Schwer, Petra.
- [Multi angle] Quiver Grassmannians of Dynkin type / Author of the conference Cerulli-Irelli, Giovanni.
- [Multi angle] Weighted Schur algebras or «Diagrammatic Cherednik algebras» over fields of arbitrary characteristic / Author of the conference Bowman, Christopher David.
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
