On the cyclotomic Hecke algebras of complex reflection groups

Maria Chlouveraki

Home/Archive/arXiv

arXiv · 0710.0776

On the cyclotomic Hecke algebras of complex reflection groups

Maria Chlouveraki

View original source ↗Read source document ↗Export metadata ↓

Abstract

Following the definition of Rouquier for the "families of characters" of a Weyl group and its generalization to the case of complex reflection groups, already appeared in the works of Broue-Kim and Malle-Rouquier, we show that these "families" depend on a numerical datum of the group, its "essential hyperplanes". Using this characterization, we provide the algorithm and the results of the determination of the Rouquier blocks of the cyclotomic Hecke algebras of all exceptional complex reflection groups.

Explore related subjects

math.RT

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Maria Chlouveraki. 2007-10-03. On the cyclotomic Hecke algebras of complex reflection groups. https://arxiv.org/abs/0710.0776

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

On the $θ$-split side of the local relative trace formula

The author derives an expression for one side of the local relative trace formula, at the level of Lie algebras, by combining methods of Arthur and Harish-Chandra with the structure theory for reductive symmetric spaces.

math.RT↗

arXiv2026

Semi-infinite parabolic IC-sheaf II: the Ran space version

This paper is a sequel to arXiv:2310.0638. Let G be a split reductive group. We define the parabolic semi-infinite category on the Ran version of the affine Grassmanian Gr_{G,Ran}. We study the semi-infinite parabolic IC-sheaf in this category. We provide several descriptions of this object, one as certain colimit, another as an intermediate extension in certain category. We relate the global and local semi-infinite categories of sheaves. We also relate the intersection cohomology sheaf of the Drinfeld compactification of Bun_P with the semi-infinite parabolic IC-sheaf.

math.RT↗

arXiv2026

Unipotent representations and the categorical trace of Frobenius

We give a new proof of the classification of unipotent representations for split finite groups of Lie type. To do this, we first construct an (infinity, 2)-categorification of Lusztig's map from the Hecke algebra to the asymptotic algebra. Then we use the theory of weights to show that it induces an isomorphism after applying trace of Frobenius.

math.RT↗