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# Documents  20F55 | enregistrements trouvés : 3

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## Multi angle  Calogero-Moser cellular characters: the smooth case Bonnafé, Cédric (Auteur de la Conférence) | CIRM (Editeur )

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 ...

## 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 ...

## Multi angle  Weighted Schur algebras or «Diagrammatic Cherednik algebras» over fields of arbitrary characteristic Bowman, Christopher David (Auteur de la Conférence) | CIRM (Editeur )

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.

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