Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 14 (2018), 033, 5 pages      arXiv:1711.06009      https://doi.org/10.3842/SIGMA.2018.033
Contribution to the Special Issue on the Representation Theory of the Symmetric Groups and Related Topics

The Duals of the 2-Modular Irreducible Modules of the Alternating Groups

John Murray
Department of Mathematics & Statistics, Maynooth University, Co. Kildare, Ireland

Received January 04, 2018, in final form April 04, 2018; Published online April 17, 2018

Abstract
We determine the dual modules of all irreducible modules of alternating groups over fields of characteristic 2.

Key words: symmetric group; alternating group; dual module; irreducible module; characteristic 2.

pdf (265 kb)   tex (10 kb)

References

  1. Benson D., Spin modules for symmetric groups, J. London Math. Soc. 38 (1988), 250-262.
  2. Bessenrodt C., On the representation theory of alternating groups, Algebra Colloq. 10 (2003), 241-250.
  3. Brauer R., On the connection between the ordinary and the modular characters of groups of finite order, Ann. of Math. 42 (1941), 926-935.
  4. Brauer R., Nesbitt C., On the modular characters of groups, Ann. of Math. 42 (1941), 556-590.
  5. Bressoud D.M., A combinatorial proof of Schur's 1926 partition theorem, Proc. Amer. Math. Soc. 79 (1980), 338-340.
  6. Ford B., Kleshchev A.S., A proof of the Mullineux conjecture, Math. Z. 226 (1997), 267-308.
  7. James G.D., The representation theory of the symmetric groups, Lecture Notes in Math., Vol. 682, Springer, Berlin, 1978.
  8. James G.D., Kerber A., The representation theory of the symmetric group, Encyclopedia of Mathematics and its Applications, Vol. 16, Addison-Wesley Publishing Co., Reading, Mass., 1981.
  9. Schur I., Zur additiven Zahlentheorie, Sitzungsber. Preuß. Akad. Wiss. Phys.-Math. Kl. (1926), 488-495, Reprinted in Schur I., Gesammelte Abhandlungen, Band III, Springer-Verlag, Berlin - New York, 1973, 43-50.

Previous article  Next article   Contents of Volume 14 (2018)