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Documents  20C08 | enregistrements trouvés : 6

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Let $p$ be a prime number and $F$ be a non-archimedean field with finite residue class field of characteristic $p$. Understanding the category of Iwahori-Hecke modules for $SL_2(F)$ is of great interest in the study of $p$-modular smooth representations of $SL_2(F)$, as these modules naturally show up as spaces of invariant vectors under the action of the standard pro-$p$-Iwahori subgroup. In this talk, we will discuss a work in progress in which we aim to classify all non-trivial extensions between these modules and to compare them with their analogues for $p$-modular smooth representations of $SL_2(F)$ and with their Galois counterpart in the setting of the local Langlands correspondences in natural characteristic.
Let $p$ be a prime number and $F$ be a non-archimedean field with finite residue class field of characteristic $p$. Understanding the category of Iwahori-Hecke modules for $SL_2(F)$ is of great interest in the study of $p$-modular smooth representations of $SL_2(F)$, as these modules naturally show up as spaces of invariant vectors under the action of the standard pro-$p$-Iwahori subgroup. In this talk, we will discuss a work in progress in ...

11F70 ; 11F85 ; 20C08 ; 20G05 ; 22E50

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Spherical Hecke algebra, Satake transform, and an introduction to local Langlands correspondence.
CIRM - Chaire Jean-Morlet 2016 - Aix-Marseille Université

20C08 ; 22E50 ; 11S37

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In geometric representation theory, one is interested in studying the geometry of affine Grassmannians of quasi-split simply-connected reductive groups. In this endeavor, one of the main techniques, introduced by Faltings in the split case, consists in constructing natural realisations of these ind-schemes over the integers. In the twisted case, this was done by Pappas and Rapoport in the tamely ramified case, i.e. over $\mathbb{Z}[1/e]$, where $e = 2$ or $3$ is the order of the automorphism group of the split form we are dealing with. We explain how to extend the parahoric group scheme that appeared in work of Pappas, Rapoport, Tits and Zhu to the polynomial ring $\mathbb{Z}[t]$ with integer coefficients and additionally how the group scheme obtained in char. $e$ can be regarded as a parahoric model of a basic exotic pseudo-reductive group. Then we study the geometry of the affine Grassmannian and also its global deformation à la Beilinson-Drinfeld, recovering all the known results in the literature away from $e = 0$. This also has some pertinence to the study of local models of Shimura varieties in wildly ramified cases.
In geometric representation theory, one is interested in studying the geometry of affine Grassmannians of quasi-split simply-connected reductive groups. In this endeavor, one of the main techniques, introduced by Faltings in the split case, consists in constructing natural realisations of these ind-schemes over the integers. In the twisted case, this was done by Pappas and Rapoport in the tamely ramified case, i.e. over $\math...

20G44 ; 20C08

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Multi angle  Affine Springer fibers and G1T modules
Vasserot, Eric (Auteur de la Conférence) | CIRM (Editeur )

I will explain a relation between the center of the category of G1T modules and the cohomology of affine Springer fibers, and I'll discuss several related conjectures.
This is a joint work with P. Shan.

20C08 ; 14M15

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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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Multi angle  Report on the BMR freeness conjecture
Marin, Ivan (Auteur de la Conférence) | CIRM (Editeur )

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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