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Cones of highest weight vectors, weight polytopes, and Lusztig's q-analog

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Abstract

We relate the invariant theory of cones of highest weight vectors to weight multiplicities and theirq-analogs. Whenever the action of a maximal torus on the coneCλ* has some nice properties, we obtain simple closed formulas for all weight multiplicities and theirq-analogs in the representationsV nλ ,n∈ℕ. We find a connection between the character ofV nλ and the respective weight polytopes.

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Authors and Affiliations

  1. ul. akad. Anokhina, d. 30, kor. 1, kv. 7, 117602, Moscow, Russia

    D. Panyushev

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  1. D. Panyushev
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This research was supported in part by the Alexander von Humboldt Foundation and INTAS Grant No. 93-0893

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Panyushev, D. Cones of highest weight vectors, weight polytopes, and Lusztig's q-analog. Transformation Groups 2, 91–115 (1997). https://doi.org/10.1007/BF01234632

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