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Research Articles

Minimum codimension of eigenspaces in irreducible representations of simple classical linear algebraic groups

Pages 2558-2597 | Received 16 Dec 2022, Accepted 02 Jan 2024, Published online: 23 Jan 2024

References

  • Carter, R. W. (1989). Simple Groups of Lie Type. Wiley Classics Library. London: Wiley.
  • Gordeev, N. L. (1991). Coranks of elements of linear groups and the complexity of algebras of invariants. Leningrad Math. J. 2:245–267.
  • Gow, R., Laffey, T. J. (2006). On the decomposition of the exterior square of an indecomposable module of a cyclic p-group. J. Group Theory 9(5):659–672.
  • Guralnick, R. M., Saxl, J. (2003). Generation of finite almost simple groups by conjugates. J. Algebra 268(2):519–571. DOI: 10.1016/S0021-8693(03)00182-0.
  • Guralnick, R. M., Lawther, R. (2019). Generic stabilizers in actions of simple algebraic groups i: modules and the first grassmanian varieties. arXiv: Group Theory.
  • Hall, J. I., Liebeck, M. W., Seitz, G. M. (1992). Generators for finite simple groups, with applications to linear groups. Q. J. Math. 43(4):441–458. DOI: 10.1093/qmathj/43.4.441.
  • Humphreys, J. E. (1972). Introduction to Lie Algebras and Representation Theory. Graduate Texts in Mathematics. New York: Springer.
  • Jantzen, J. C. (2007). Representations of Algebraic Groups. Mathematical Surveys and Monographs. Providence, RI: American Mathematical Society.
  • Kac, V. G., Watanabe, K. (1982). Finite linear groups whose ring of invariants is a complete intersection. Bull. Amer. Math. Soc. 6:221–223. DOI: 10.1090/S0273-0979-1982-14989-8.
  • Kemper, G., Malle, G. (1997). The finite irreducible linear groups with polynomial ring of invariants. Transformation Groups 2:57–89. DOI: 10.1007/BF01234631.
  • Korhonen, M. (2019). Jordan blocks of unipotent elements in some irreducible representations of classical groups in good characteristic. Proc. Amer. Math. Soc. 147(10):4205–4219. DOI: 10.1090/proc/14570.
  • Korhonen, M. (2020). Hesselink normal forms of unipotent elements in some representations of classical groups in characteristic two. J. Algebra 559:268–319. DOI: 10.1016/j.jalgebra.2020.03.035.
  • Lübeck, F. (2001). Small degree representations of finite Chevalley groups in defining characteristic. LMS J. Comput. Math. 4:135–169. http://www.math.rwth-aachen.de/Frank.Luebeck/chev/WMSmall/index.html. DOI: 10.1112/S1461157000000838.
  • Lübeck, F. (2001). Tables of weight multiplicities.
  • Liebeck, M. W., Seitz, G. M. (2012). Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras. Mathematical Surveys and Monographs. Providence, RI: American Mathematical Society.
  • Malle, G., Testerman, D. (2011). Linear Algebraic Groups and Finite Groups of Lie Type. Cambridge Studies in Advanced Mathematics. Cambridge, UK: Cambridge University Press.
  • Martínez, A. L. (2018). Low-dimensional irreducible rational representations of classical algebraic groups. DOI: 10.48550/ARXIV.1811.07019.
  • McNinch, G. J. (1998). Dimensional criteria for semisimplicity of representations. Proc. London Math. Soc. 76(1):95–149. DOI: 10.1112/S0024611598000045.
  • Seitz, G. M. (1987). The Maximal Subgroups of Classical Algebraic Groups, 365. Providence, RI: American Mathematical Society.
  • Smith, S. D. (1982). Irreducible modules and parabolic subgroups. J. Algebra 75(1):286–289. DOI: 10.1016/0021-8693(82)90076-X.
  • Steinberg, R. (2016). Lectures on Chevalley Groups. University Lecture Series, Vol. 66. Providence, RI: American Mathematical Society.
  • Suprunenko, I. D. (1983). Preservation of systems of weights of irreducible representations of an algebraic group and a Lie algebra of type A with bounded higher weights in reduction modulo p. Vestsi Akad. Na uk BSSR, Ser. Fiz.-Mat. Na uk (2):18–22.
  • Verbitsky, M. (1999). Holomorphic symplectic geometry and orbifold singularities. Asian J. Math. 4:553–564. DOI: 10.4310/AJM.2000.v4.n3.a4.