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Documents  Littelmann, Peter | enregistrements trouvés : 6

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Research talks;Algebra;Geometry;Number Theory

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. 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 ...

06B15 ; 05A19 ; 55R80

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- x; 763 p.
ISBN 978-3-03719-171-2

Series of congress reports

Localisation : Colloque 1er étage (BAD)

groupe algébrique # représentation bornée et semi-bornée # catégorisation # formule de caractères # algèbre à grappes # théorie de Deligne-Lusztig # dégénérescence plate # géométrisation # haute catégorie pondérée # groupe de Lie de dimension infinie # conjecture local-global # variété spéciale # théorie topologique des champs

14Mxx ; 16Gxx ; 17Bxx ; 18Exx ; 20Gxx ; 22Exx ; 58Cxx ; 81Txx

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Research talks;Algebra

We begin by introducing to the diagrammatic Cherednik algebras of Webster. We then summarise some recent results (in joint work with Anton Cox and Liron Speyer) concerning the representation theory of these algebras. In particular we generalise Kleshchev-type decomposition numbers, James-Donkin row and column removal phenomena, and the Kazhdan-Lusztig approach to calculating decomposition numbers.

20G43 ; 20F55 ; 20B30

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Research talks;Algebra;Combinatorics

We present a new approach to affine Deligne Lusztig varieties which allows us to study the so called "non-basic" case in a type free manner. The central idea is to translate the question of non-emptiness and the computation of the dimensions of these varieties into geometric questions in the Bruhat-Tits building. All boils down to understand existence of certain positively folded galleries in affine Coxeter complexes. To do so, we explicitly construct such galleries and use, among other techniques, the root operators introduced by Gaussent and Littelmann to manipulate them. We present a new approach to affine Deligne Lusztig varieties which allows us to study the so called "non-basic" case in a type free manner. The central idea is to translate the question of non-emptiness and the computation of the dimensions of these varieties into geometric questions in the Bruhat-Tits building. All boils down to understand existence of certain positively folded galleries in affine Coxeter complexes. To do so, we explicitly ...

14L30 ; 14M15 ; 20G05

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Research talks;Algebra

Given a finite-dimensional representation M of a Dynkin quiver Q (which is the orientation of a simply-laced Dynkin diagram) we attach to it the variety of its subrepresentations. This variety is strati ed according to the possible dimension vectors of the subresentations of M. Every piece is called a quiver Grassmannian. Those varieties were introduced by Schofield and Crawley Boevey for the study of general representations of quivers. As pointed out by Ringel, they also appeared previously in works of Auslander.
They reappered in the literature in 2006, when Caldero and Chapoton proved that they can be used to categorify the cluster algebras associated with Q. A special case is when M is generic. In this case all the quiver Grassmannians are smooth and irreducible of "minimal dimension". On the other hand, in collaboration with Markus Reineke and Evgeny Feigin, we showed that interesting varieties appear as quiver Grassmannians associated with non-rigid modules. In this talk I will survey on recent progresses on the subject. In particular I will provide another proof of the key result of Caldero and Chapoton.
Given a finite-dimensional representation M of a Dynkin quiver Q (which is the orientation of a simply-laced Dynkin diagram) we attach to it the variety of its subrepresentations. This variety is strati ed according to the possible dimension vectors of the subresentations of M. Every piece is called a quiver Grassmannian. Those varieties were introduced by Schofield and Crawley Boevey for the study of general ...

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- 29 p.

Localisation : Ouvrage RdC (LITT)

algèbre de Kac-Moody # algèbre de Lie complexe semi- simple # combinatoire # groupe algébrique # représentation # représentation de groupe symmétrique # variété

20B30 ; 20Cxx ; 20D08 ; 22E30 ; 22E65

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