A lower bound for the dimension of a highest weight module

Goldstein, Daniel; Guralnick, Robert; Stong, Richard

doi:10.1090/ert/509

A lower bound for the dimension of a highest weight module
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by Daniel Goldstein, Robert Guralnick and Richard Stong

Represent. Theory 21 (2017), 611-625

DOI: https://doi.org/10.1090/ert/509

Published electronically: December 19, 2017

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Abstract:

For each integer $t>0$ and each simple Lie algebra $\mathfrak {g}$, we determine the least dimension of an irreducible highest weight representation of $\mathfrak {g}$ whose highest weight has width $t$. As a consequence, we classify all irreducible modules whose dimension equals a product of two primes. This consequence, which was in fact the driving force behind our paper, answers a question of N. Katz.

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