Crystal graphs of higher level q-deformed Fock spaces, Lusztig a-values and Ariki-Koike algebras

Details Crystal graphs of higher level q-deformed Fock spaces, Lusztig a-values and Ariki-Koike algebras Crystal graphs of higher level q-deformed Fock spaces, Lusztig a-values and Ariki-Koike algebras

2005-04-13

arxiv.org/abs/math/0504267v3

Mathematics

Representation Theory

Scientific paper

We show that the different labelings of the crystal graph for irreducible
highest weight $\mathcal{U}\_q (\hat{\mathfrak{sl}}\_e)$-modules lead to
different labelings of the simple modules for non semisimple Ariki-Koike
algebras by using Lusztig $a$-values.

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