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

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

2011-01-07

arxiv.org/abs/1101.1465v1

Mathematics

Representation Theory

Scientific paper

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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