Abstract
We prove a q-analogue of the Carter–Payne theorem in the case where the differences between the parts of the partitions are sufficiently large. We identify a layer of the Jantzen filtration which contains the image of these Carter–Payne homomorphisms and we show how these homomorphisms compose.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Bergeron, F., Bergeron, N., Howlett, R.B., Taylor, D.E.: A decomposition of the descent algebra of a finite Coxeter group. J. Algebraic Comb. 1, 23–44 (1992)
Carter, R.W., Lusztig, G.: On the modular representations of the general linear and symmetric groups. Math. Z. 136, 193–242 (1974)
Carter, R.W., Payne, M.T.J.: On homomorphisms between Weyl modules and Specht modules. Math. Proc. Camb. Philos. Soc. 87, 419–425 (1980)
Dipper, R., James, G.: Representations of Hecke algebras of general linear groups. Proc. Lond. Math. Soc. 52(3), 20–52 (1986)
Dixon, J.: Some results concerning Verma modules. Ph.D. Thesis, Queen Mary College, University of London (2008)
Donkin, S.: Tilting modules for algebraic groups and finite dimensional algebras. In: Happel, D., Krause, H. (eds.) A Handbook of Tilting Theory. London Math. Soc. Lecture Notes Series, vol. 332, pp. 215–257. Cambridge University Press, Cambridge (2007)
Ellers, H., Murray, J.: Branching rules for Specht modules. J. Algebra 307(1), 278–286 (2007)
Ellers, H., Murray, J.: Carter–Payne homomorphisms and branching rules for endomorphism rings of Specht modules. J. Group Theory (in press). doi:10.1515/JGT.2010.002
Fayers, M., Martin, S.: Homomorphisms between Specht modules. Math. Z. 248, 395–421 (2004)
James, G.: The Representation Theory of the Symmetric Groups. SLN, vol. 682. Springer, New York (1978)
Lyle, S., Mathas, A.: Row and column removal theorems for homomorphisms of Specht modules and Weyl modules. J. Algebraic Comb. 22, 151–179 (2005)
Mathas, A.: Hecke Algebras and Schur Algebras of the Symmetric Group. Univ. Lecture Notes, vol. 15. AMS, Providence (1999)
Murphy, G.: A new construction of Young’s seminormal representation of the symmetric group. J. Algebra 69, 287–291 (1981)
Murphy, G.: The representations of Hecke algebras of type A n . J. Algebra 173(1), 97–121 (1995)
Parker, A.: Good l-filtrations for q-GL3(k). J. Algebra 304, 157–189 (2006)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Lyle, S., Mathas, A. Carter–Payne homomorphisms and Jantzen filtrations. J Algebr Comb 32, 417–457 (2010). https://doi.org/10.1007/s10801-010-0222-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10801-010-0222-z