Documents  20C08 | enregistrements trouvés : 35

Research talks;Lie Theory and Generalizations;Number Theory

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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- 158 p.
ISBN 978-90-277-1743-6

Nato a.s.i. series

Localisation : Colloque 1er étage (ANTW)

13-06 ; 13Cxx ; 13Exx ; 14Cxx ; 20C08

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- 494 p.
ISBN 978-0-8176-4342-3

Progress in mathematics , 0243

Localisation : Collection 1er étage

théorie de la représentation # algèbre de Lie semi-simple # représentation d'algèbre de Lie # Antony Joseph # groupe quantique # anneau d'opérateur différentiel # action de groupe # algèbre enveloppante # anneau gradué # algèbre de Lie de dimension infinie # opérateur de vertex # algèbre de Hecke # cohomologie # analyse sur les groupes de Lie p-adiques # module # microlocalisation # variété de Poisson

13N10 ; 14L30 ; 14R20 ; 16K40 ; 16S30 ; 16S32 ; 16S36 ; 16S40 ; 16W50 ; 17B35 ; 17B37 ; 17B65 ; 17B69 ; 20C08 ; 20G10 ; 22D20 ; 22E35 ; 32C38 ; 33C45 ; 35A27 ; 53D17

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- 154 p.
ISBN 978-0-8218-3701-6

Contemporary mathematics , 0392

Localisation : Collection 1er étage

représentation d'algèbre # représentation de groupe # géométrie algébrique # algèbre homologique # groupe quantique # invariant de Gromov-Witten # algèbre de Hecke # groupe quantique # représentation modulaire # paramétrisation # algèbre de Lie de dimension infinie

20-06 ; 16-06 ; 17-06 ; 14C05 ; 14N35 ; 16E40 ; 16G20 ; 16G60 ; 17B37 ; 17B69 ; 20C08 ; 82B23

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- 254 p.
ISBN 978-0-8218-3924-9

Contemporary mathematics , 0413

Localisation : Collection 1er étage

représentation de groupe # groupe algébrique affine # groupe quantique # algèbre de Lie

05E10 ; 14L17 ; 16G20 ; 17Bxx ; 20C08 ; 20Gxx

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- xv; 295 p.
ISBN 978-0-8218-4555-4

Contemporary mathematics , 0478

Localisation : Collection 1er étage

représentation d'algebre # représentation de groupe

16Gxx ; 17Bxx ; 20Cxx ; 20Gxx ; 17B10 ; 17B20 ; 17B37 ; 17B45 ; 17B56 ; 20G05 ; 20G10 ; 20G42 ; 20C05 ; 20C08 ; 20C30

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- xi; 310 p.
ISBN 978-0-8218-6917-8

Proceedings of symposia in pure mathematics , 0086

Localisation : Collection 1er étage

algèbre de Lie # représentations de groupes

17B37 ; 17B55 ; 17B56 ; 17B65 ; 17B67 ; 20C08 ; 20C11 ; 20G05 ; 20G42 ; 00B25 ; 17-06 ; 20-06 ; 17Bxx ; 20Cxx

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- pag. mult.

Séminaire Bourbaki mars 2016

Localisation : Séminaire 1er étage

équation de Monge-Ampère complexe # variété kählérienne # géodésique minimisante # singulière minimisante # géométrie sous-riemannienne # propriété de non-indépendance # mesure de Keisler # théorie de Hodge # théorème de décomposition

32W20 ; 32Q20 ; 49Q20 ; 03C45 ; 28E05 ; 20C08 ; 14C30

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- xii; 355 p.
ISBN 978-1-4704-1844-1

Proceedings of symposia in pure mathematics , 0092

Localisation : Collection 1er étage

algèbre de Lie # superalgèbre de Lie # algèbre d'opérateurs des sommets

17B37 ; 17B55 ; 17B56 ; 17B65 ; 17B67 ; 17B69 ; 20C08 ; 20C11 ; 20G05 ; 20G42

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- iii; 188 p.
ISBN 978-1-57146-331-9

Localisation : Colloque 1er étage (CAMB)

métrique de Kähler-Einstein # géométrie algébrique # modèle de Potts # transition de phase # algèbre de Hecke # groupe $p$-adique # fonction de Green # équation de Painlevé

00B25 ; 32Q20 ; 82B26 ; 82B20 ; 20C08 ; 20C11 ; 34B27 ; 34M55

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- x; 361 p.
ISBN 978-1-4704-2460-2

Contemporary mathematics , 0683

Localisation : Collection 1er étage

catégorie dérivée # théorie quantique # algèbre non associative # algèbre de Lie # théorie des groupes # représentation # algèbre de Hecke # cohomologie # catégorie monoïdale # algèbre de Kac-Moody

81R50 ; 17B10 ; 20C08 ; 14F05 ; 18D10 ; 17B50 ; 17B55 ; 17B67 ; 81-06 ; 17-06

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- x; 267 p.
ISBN 978-1-4704-2821-1

Contemporary mathematics , 0684

Localisation : Collection 1er étage

catégorie dérivée # théorie quantique # topologie # géométrie algébrique # cohomologie # catégorie monoïdale # opérateur différentiel # invariant # algèbre non associative # algèbre de Lie # algèbre de Hecke # algèbre de Kac-Moody

81R50 ; 57M25 ; 14F05 ; 18D10 ; 58J28 ; 17B81 ; 20C08 ; 17B55 ; 17B67 ; 81-06

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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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Research talks

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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Research talks

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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- 446 p.
ISBN 978-0-19-850250-0

London mathematical society monographs new series , 0021

Localisation : Ouvrage RdC (GECK)

algèbre de Hecke # calcul # caractère # caractère induit # caractère irréductible # classe de conjugaison # groupe de Coxeter # matrice de Cartan # monoïde tressé # représentation d'algèbre # sous-groupe parabolique # symétrie d'algèbre # théorie des groupes # valeur de caractère

20C08 ; 20C15

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- 158 p.
ISBN 978-0-8218-3232-5

University lecture series , 0026

Localisation : Collection 1er étage

groupe quantique # représentation de groupe # espace topologique linéaire # tableau de Young # algèbre quantique # algèbre de Hecke

05E10 ; 17B37 ; 17B67 ; 20C08

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- 253 p.
ISBN 978-1-57146-079-0

Localisation : Ouvrage RdC (Curr)

groupe de réflection # mécanique des fluides # hydrodynamique # groupe de tresses # algèbre de Hecke # progression arithmétique # variété algébrique réelle # topologie # mouvement brwonien # processus stochastique

00B15 ; 20C08 ; 20F36 ; 76W05 ; 11B25 ; 14P25 ; 60J65

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