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A Combinatorial Character Formula for Some Highest Weight Modules

Published online by Cambridge University Press:  04 December 2007

OLIVIER MATHIEU  and
GEORGES PAPADOPOULO
OLIVIER MATHIEU
Affiliation:
Université Louis Pasteur, IRMA, 7 rue René Descartes, 67000 Strasbourg France. e-mail: [email protected], [email protected]
GEORGES PAPADOPOULO
Affiliation:
Université Louis Pasteur, IRMA, 7 rue René Descartes, 67000 Strasbourg France. e-mail: [email protected], [email protected]
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Abstract

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We give a combinatorial formula for the weight multiplicities of some infinite-dimensional highest weight ${\mathfrak g}$${\mathfrak l}$ (n)-modules. Our proof, which does not rely on Kazhdan–Lusztig combinatorics, uses a reduction to finite characteristics. The character formula for the corresponding modular representations, which has been computed in a 1997 preprint by the authors, is based on a dual pair which has no obvious counterpart in characteristic zero.

Keywords

Character formulahighest weight modules.
Type
Research Article
Information
Compositio Mathematica , Volume 117 , Issue 2 , June 1999 , pp. 153 - 159
Copyright
© 1999 Kluwer Academic Publishers