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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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A lower bound for the dimension of a highest weight module
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by Daniel Goldstein, Robert Guralnick and Richard Stong PDF
Represent. Theory 21 (2017), 611-625


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.
  • Wieb Bosma, John Cannon, and Catherine Playoust, The Magma algebra system. I. The user language, J. Symbolic Comput. 24 (1997), no. 3-4, 235–265. Computational algebra and number theory (London, 1993). MR 1484478, DOI 10.1006/jsco.1996.0125
  • N. Bourbaki, Éléments de mathématique. Fasc. XXXIV. Groupes et algèbres de Lie. Chapitre IV: Groupes de Coxeter et systèmes de Tits. Chapitre V: Groupes engendrés par des réflexions. Chapitre VI: systèmes de racines, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1337, Hermann, Paris, 1968 (French). MR 0240238
  • E. Breuillard and G. Pisier, Remarks on random unitaries and amenable linear groups, in preparation.
  • William Fulton and Joe Harris, Representation theory, Graduate Texts in Mathematics, vol. 129, Springer-Verlag, New York, 1991. A first course; Readings in Mathematics. MR 1153249, DOI 10.1007/978-1-4612-0979-9
  • Roe Goodman and Nolan R. Wallach, Representations and invariants of the classical groups, Encyclopedia of Mathematics and its Applications, vol. 68, Cambridge University Press, Cambridge, 1998. MR 1606831
  • Kathryn E. Hare, The size of characters of compact Lie groups, Studia Math. 129 (1998), no. 1, 1–18. MR 1611918, DOI 10.4064/sm-129-1-1-18
  • Jens Carsten Jantzen, Low-dimensional representations of reductive groups are semisimple, Algebraic groups and Lie groups, Austral. Math. Soc. Lect. Ser., vol. 9, Cambridge Univ. Press, Cambridge, 1997, pp. 255–266. MR 1635685
  • Nicholas M. Katz, Exponential sums and differential equations, Annals of Mathematics Studies, vol. 124, Princeton University Press, Princeton, NJ, 1990. MR 1081536, DOI 10.1515/9781400882434
  • Nicholas M. Katz, Gauss sums, Kloosterman sums, and monodromy groups, Annals of Mathematics Studies, vol. 116, Princeton University Press, Princeton, NJ, 1988. MR 955052, DOI 10.1515/9781400882120
  • Nicholas M. Katz, Convolution and equidistribution, Annals of Mathematics Studies, vol. 180, Princeton University Press, Princeton, NJ, 2012. Sato-Tate theorems for finite-field Mellin transforms. MR 2850079
  • Frank Lübeck, Small degree representations of finite Chevalley groups in defining characteristic, LMS J. Comput. Math. 4 (2001), 135–169. MR 1901354, DOI 10.1112/S1461157000000838
  • Robert Steinberg, Lectures on Chevalley groups, Yale University, New Haven, Conn., 1968. Notes prepared by John Faulkner and Robert Wilson. MR 0466335
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Additional Information
  • Daniel Goldstein
  • Affiliation: Center for Communications Research, San Diego, California 92121
  • MR Author ID: 709300
  • Email:
  • Robert Guralnick
  • Affiliation: Department of Mathematics, University of Southern California, Los Angeles, California 90089-2532
  • MR Author ID: 78455
  • Email:
  • Richard Stong
  • Affiliation: Center for Communications Research, San Diego, California 92121
  • MR Author ID: 167705
  • Email:
  • 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:
  • MathSciNet review: 3738091