Weyl module

In algebra, a Weyl module is a representation of a reductive algebraic group, introduced by Carter and Lusztig (1974, 1974b) and named after Hermann Weyl. In characteristic 0 these representations are irreducible, but in positive characteristic they can be reducible, and their decomposition into irreducible components can be hard to determine.

See also

• Borel–Weil–Bott theorem
• Garnir relations

Further reading

• Carter, Roger W.; Lusztig, George (1974), "On the modular representations of the general linear and symmetric groups", Mathematische Zeitschrift, 136 (3): 193–242, doi:10.1007/BF01214125, ISSN 0025-5874, MR 0354887, S2CID 186230432
• Carter, Roger W.; Lusztig, G. (1974b), "On the modular representations of the general linear and symmetric groups", Proceedings of the Second International Conference on the Theory of Groups (Australian Nat. Univ., Canberra, 1973), Lecture Notes in Mathematics, vol. 372, Berlin, New York: Springer-Verlag, pp. 218–220, doi:10.1007/BFb0065172, ISBN 978-3-540-06845-7, MR 0369503
• Dipper, R. (2001) [1994], "Weyl_module", Encyclopedia of Mathematics, EMS Press