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
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.References
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Bibliographic Information
- Daniel Goldstein
- Affiliation: Center for Communications Research, San Diego, California 92121
- MR Author ID: 709300
- Email: danielgolds@gmail.com
- Robert Guralnick
- Affiliation: Department of Mathematics, University of Southern California, Los Angeles, California 90089-2532
- MR Author ID: 78455
- Email: guralnic@usc.edu
- Richard Stong
- Affiliation: Center for Communications Research, San Diego, California 92121
- MR Author ID: 167705
- Email: stong@ccrwest.org
- Received by editor(s): April 1, 2016
- Received by editor(s) in revised form: August 11, 2017
- Published electronically: December 19, 2017
- Additional Notes: The second author was partially supported by NSF grants DMS-1302886 and DMS-1600056.
- © Copyright 2017 Institute for Defense Analyses
- Journal: Represent. Theory 21 (2017), 611-625
- MSC (2010): Primary 17B10, 22E46
- DOI: https://doi.org/10.1090/ert/509
- MathSciNet review: 3738091