The cyclotomic Jantzen-Schaper theorem
Gordon James and Andrew Mathas
Research Report 98-2
Date: 12 January 1998
In this paper we use the cyclotomic q-Schur algebras to prove an
analogue of the Jantzen-Schaper theorem for the Ariki-Koike algebras. Most of
the argument is devoted to first proving an analogue of Jantzen's sum formula
for the Weyl modules of the cyclotomic q-Schur algebra. The result
for the Ariki-Koike algebras is then deduced by a Schur functor argument. As
a corollary of these results we obtain criteria for the Weyl modules and
Specht modules of these algebras to be irreducible.
As a special case of our results we obtain, for the first
time, an analogue of the Jantzen-Schaper theorem for Coxeter groups of
Ariki-Koike algebras. cyclotomic q-Schur algebras.
AMS Subject Classification (1991)
Secondary: 20C20, 20G05
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