Proceedings of Symposia in Pure MathematicsVolume 00 , 19 xx Simple modules of Ariki
نویسندگان
چکیده
In this note we classify the simple modules of the Ariki{Koike algebras when q = 1 and also describe the classiication for those algebras considered in 3, 14], together with the underlying computation of the computing canonical bases of an aane quantum group. In particular, this gives a classiication of the simple modules of the Iwahori{Hecke algebras of type B.
منابع مشابه
On the classification of simple modules for cyclotomic Hecke algebras of type G(m, 1, n) and Kleshchev multipartitions
We give a proof of a conjecture that Kleshchev multipartitions are those partitions which parametrize non-zero simple modules obtained as factor modules of Specht modules by their own radicals.
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The Ariki-Koike algebras were introduced by Ariki and Koike [8] who were interested in them because they are a natural generalization of the Iwahori-Hecke algebras of types A and B. At almost the same time, Broué and Malle [21] attached to each complex reflection group a cyclotomic Hecke algebra which, they conjectured, should play a role in the decomposition of the induced cuspidal representat...
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Let H be a non semi-simple Ariki-Koike algebra. According to [19] and [15], there is a generalisation of Lusztig’s a-function which induces a natural combinatorial order (parametrised by a tuple m) on Specht modules. In some cases, Geck and Jacon have proved that this order makes unitriangular the decomposition matrix of H . The algebra H is then said to admit a "canonical basic set". We fully ...
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