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Documents  Kessar, Radha | enregistrements trouvés : 6

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Research talks;Lie Theory and Generalizations;Number Theory

22E50 ; 11F85 ; 11F70

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Research talks;Algebraic and Complex Geometry

In this joint work with Jacques Thévenaz, we develop the representation theory of finite sets and correspondences : let kC the category of finite sets, in which morphisms are k-linear combinations of correspondences (where k is a given commutative ring), and let Fk be the category of correspondence functors (over k), i.e. the category of k-linear functors from kC to k-modules. This category Fk is an abelian k-linear category. In such a framework, it is of crucial importance to describe the algebra of essential endomorphisms of a given object. This is what we achieved in a previous work on the algebra of essential relations on a finite set, describing in particular its simple modules. This description leads to a parametrization of the simple functors on kC by triples (E;R;V) consisting of a finite set E, a partial order relation R on E, and a simple k-linear representation V of the automorphism group of (E;R). In this joint work with Jacques Thévenaz, we develop the representation theory of finite sets and correspondences : let kC the category of finite sets, in which morphisms are k-linear combinations of correspondences (where k is a given commutative ring), and let Fk be the category of correspondence functors (over k), i.e. the category of k-linear functors from kC to k-modules. This category Fk is an abelian k-linear category. In such a ...

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Research talks;Algebraic and Complex Geometry

Using the representation theory of Cherednik algebra at t= 0, we define a family of "Calogero-Moser cellular characters" for any complex reflection group $W$. Whenever $W$ is a Coxeter group, we conjecture that they coincide with the "Kazhdan-Lusztig cellular characters". We shall give some evidences for this conjecture. Our main result is that, whenever the associated Calogero-Moser space is smooth, then all the Calogero-Moser cellular characters are irreducible. This implies in particular that our conjecture holds in type $A$ and for some particular choices of the parameters in type $B$. Using the representation theory of Cherednik algebra at t= 0, we define a family of "Calogero-Moser cellular characters" for any complex reflection group $W$. Whenever $W$ is a Coxeter group, we conjecture that they coincide with the "Kazhdan-Lusztig cellular characters". We shall give some evidences for this conjecture. Our main result is that, whenever the associated Calogero-Moser space is smooth, then all the Calogero-Moser cellular ...

20C08 ; 20F55 ; 05E10

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Research talks;Algebra

I will present arguably the most basic one among the set of conjectures stated in 1998 by Broue, Malle and Rouquier (following early work by Broue and Malle) about the generalized Iwahori-Hecke algebras associated to complex reflection groups. By a combination of several kind of arguments and lots of hand-writen as well as computer-assisted calculations, it seems that a complete proof is now within reach. I will report on recent progress by my PhD student E. Chavli, as well as on a recent work by G. Pfeiffer and myself on this topic. I will present arguably the most basic one among the set of conjectures stated in 1998 by Broue, Malle and Rouquier (following early work by Broue and Malle) about the generalized Iwahori-Hecke algebras associated to complex reflection groups. By a combination of several kind of arguments and lots of hand-writen as well as computer-assisted calculations, it seems that a complete proof is now within reach. I will report on recent progress by my ...

20F55 ; 20C08

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- viii; 361 p.
ISBN 978-3-03719-185-9

EMS series of lectures in mathematics

Localisation : Ouvrage RdC (LOCA)

groupe réductif fini # variété de Deligne-Lusztig # bloc de Brauer # conjecture locale-globale # taille de la base # ratio à point fixe # marche aléatoire

20Bxx ; 20Cxx ; 20Gxx ; 20-06 ; 20D05 ; 20E32 ; 20G25 ; 00B15

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- vi; 320 p.
ISBN 978-1-107-60100-0

London mathematical society lecture note series , 0391

Localisation : Collection 1er étage

algèbre de fusion # système de fusion # structure locale d'un groupe fini # homotopie # représentation modulaire des groupes

20-02 ; 20C20 ; 20D20 ; 55R35 ; 55R40 ; 20C33 ; 20D60 ; 20J15 ; 55Q99 ; 55P99

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