Maria Chlouveraki
Decomposition matrices for $d$-Harish-Chandra series: the exceptional rank two cases.
Mon, 08/23/2010 - 15:01 — SomNambulAuthors: Maria Chlouveraki, Hyohe Miyachi
Subjects: Representation Theory
AbstractWe calculate all decomposition matrices of the cyclotomic Hecke algebras of
the rank 2 exceptional complex reflection groups in characteristic 0. We prove
the existence of canonical basic sets in the sense of Geck-Rouquier and show
that all modular irreducible representations can be lifted to the ordinary
ones.Rouquier blocks of the cyclotomic Hecke algebras of G(de,e,r).
Mon, 11/30/2009 - 16:01 — SomNambulAuthors: Maria Chlouveraki
Subjects: Representation Theory
AbstractThe "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.Schur elements and basic sets for cyclotomic Hecke algebras.
Tue, 10/27/2009 - 16:01 — SomNambulAuthors: Nicolas Jacon, Maria Chlouveraki
Subjects: Representation Theory
AbstractWe 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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