arXiv subjects

Maria Chlouveraki

Publications and source records attributed to Maria Chlouveraki.

27 records · Page 2Linked to original sources

arXiv2011

Blocks and families for cyclotomic Hecke algebras

The families of characters, defined by Lusztig for Weyl groups, play an important role in the representation theory of finite reductive groups. The definition of Rouquier for the families of characters in terms of blocks of the Hecke algebra has made possible the generalization of this notion to the case of complex reflection groups. In this article, we study the Rouquier blocks of the cyclotomic Hecke algebras and we show that they depend on numerical data determined by the generic Hecke algebra. Moreover, we provide the algorithm and the results of their determination for all exceptional complex reflection groups.

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arXiv2011

Cell modules and canonical basic sets for Hecke algebras from Cherednik algebras

In this note we are interested in labelling the irreducible representations of non-semisimple specialisations of Hecke algebras of complex reflection groups. We will use category O for the rational Cherednik algebra and the KZ functor together with elementary algebraic and combinatorial arguments to construct "canonical basic sets" in many cases. We will also show that the images of the standard modules through the KZ functor agree with the appropriate cell modules, whenever the Hecke algebra has a cellular structure.

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arXiv2011

Schur elements for the Ariki-Koike algebra and applications

We study the Schur elements associated to the simple modules of the Ariki-Koike algebra. We first give a cancellation-free formula for them so that their factors can be easily read and programmed. We then study direct applications of this result. We also complete the determination of the canonical basic sets for cyclotomic Hecke algebras of type $G(l,p,n)$ in characteristic 0.

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arXiv2011

A cancellation-free formula for the Schur elements of the Ariki-Koike algebra

Schur elements play a powerful role in the representation theory of symmetric algebras. In the case of the Ariki-Koike algebra, Schur elements are Laurent polynomials whose factors determine when Specht modules are projective irreducible and whether the algebra is semisimple. Formulas for the Schur elements of the Ariki-Koike algebra have been independently obtained first by Geck, Iancu and Malle, and later by Mathas. The aim of this note is to give a cancellation-free formula for these polynomials, so that their factors can be easily read and programmed.

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arXiv2009

Rouquier blocks of the cyclotomic Hecke algebras of G(de,e,r)

The "Rouquier blocks" of the cyclotomic Hecke algebras, introduced by Rouquier, are a substitute for the "families of characters", defined by Lusztig for Weyl groups, which can be applied to all complex reflection groups. In this article, we determine them for the cyclotomic Hecke algebras of the groups of the infinite series, G(de,e,r), thus completing their calculation for all complex reflection groups.

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arXiv2009

Schur elements and basic sets for cyclotomic Hecke algebras

We study the Schur elements and the a-function for cyclotomic Hecke algebras. As a consequence, we show the existence of canonical basic sets, as defined by Geck-Rouquier, for certain complex reflection groups. This includes the case of finite Weyl groups for all choices of parameters (in characteristic 0).

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arXiv2008

Rouquier blocks of the cyclotomic Ariki-Koike algebras

The definition of Rouquier for the families of characters of Weyl groups in terms of blocks of the associated Iwahori-Hecke algebra has made possible the generalization of this notion to the complex reflection groups. Here we give an algorithm for the determination of the "Rouquier blocks" of the cyclotomic Ariki-Koike algebras.

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arXiv2008

Degree and valuation of the Schur elements of cyclotomic Hecke algebras

Following the generalization of the notion of families of characters, defined by Lusztig for Weyl groups, to the case of complex reflection groups, thanks to the definition given by Rouquier, we show that the degree and the valuation of the Schur elements (functions A and a) remain constant on the "families" of the cyclotomic Hecke algebras of the exceptional complex reflection groups. The same result has already been obtained for the groups of the infinite series and for some special cases of exceptional groups.

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arXiv2007

On the cyclotomic Hecke algebras of complex reflection groups

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.

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