Carter-Payne homomorphisms and Jantzen filtrations
Sinéad Lyle
and Andrew Mathas
DOI: 10.1007/s10801-010-0222-z
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.
Pages: 417–457
Keywords: keywords Hecke algebras; Carter-payne homomorphisms; jantzen filtrations
Full Text: PDF
References
1. 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)
2. Carter, R.W., Lusztig, G.: On the modular representations of the general linear and symmetric groups. Math. Z. 136, 193-242 (1974)
3. Carter, R.W., Payne, M.T.J.: On homomorphisms between Weyl modules and Specht modules. Math. Proc. Camb. Philos. Soc. 87, 419-425 (1980)
4. Dipper, R., James, G.: Representations of Hecke algebras of general linear groups. Proc. Lond. Math. Soc. 52(3), 20-52 (1986)
5. Dixon, J.: Some results concerning Verma modules. Ph.D. Thesis, Queen Mary College, University of London (2008)
6. 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)
7. Ellers, H., Murray, J.: Branching rules for Specht modules. J. Algebra 307(1), 278-286 (2007)
8. Ellers, H., Murray, J.: Carter-Payne homomorphisms and branching rules for endomorphism rings of Specht modules. J. Group Theory (in press).
2. Carter, R.W., Lusztig, G.: On the modular representations of the general linear and symmetric groups. Math. Z. 136, 193-242 (1974)
3. Carter, R.W., Payne, M.T.J.: On homomorphisms between Weyl modules and Specht modules. Math. Proc. Camb. Philos. Soc. 87, 419-425 (1980)
4. Dipper, R., James, G.: Representations of Hecke algebras of general linear groups. Proc. Lond. Math. Soc. 52(3), 20-52 (1986)
5. Dixon, J.: Some results concerning Verma modules. Ph.D. Thesis, Queen Mary College, University of London (2008)
6. 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)
7. Ellers, H., Murray, J.: Branching rules for Specht modules. J. Algebra 307(1), 278-286 (2007)
8. Ellers, H., Murray, J.: Carter-Payne homomorphisms and branching rules for endomorphism rings of Specht modules. J. Group Theory (in press).
© 1992–2009 Journal of Algebraic Combinatorics
©
2012 FIZ Karlsruhe /
Zentralblatt MATH for the EMIS Electronic Edition