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A Combinatorial Character Formula for Some Highest Weight Modules
Published online by Cambridge University Press: 04 December 2007
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.
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- © 1999 Kluwer Academic Publishers
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