Carter-Payne homomorphisms for Hecke algebras
Seminar Room 1, Newton Institute
In a famous paper Carter and Payne, building on work of Carter and Lusztig, constructed a family of homomorphisms between different Specht modules and Weyl modules of the symmetric and general linear groups, respectively. In a few special cases these maps have been generalised to give corresponding maps between the q-analogues of the Specht modules and Weyl modules, however, the full q-analogue of Carter-Payne remains open. In this talk I will describe an q-analogue of the Carter-Payne maps which are indexed by partitions with "large gaps". If time permits I will also describe how to lift Carter-Payne maps to the graded setting.
This is joint work with Sinead Lyle.