Geometric interpretation of Murphy bases and an application
Representation Theory
2011-06-13 v2
Abstract
In this article we study the representations of general linear groups which arise from their action on flag spaces. These representations can be decomposed into irreducibles by proving that the associated Hecke algebra is cellular. We give a geometric interpretation of a cellular basis of such Hecke algebras which was introduced by Murphy in the case of finite fields. We apply these results to decompose representations which arise from the space of modules over principal ideal local rings of length two with a finite residue field.
Keywords
Cite
@article{arxiv.1101.2738,
title = {Geometric interpretation of Murphy bases and an application},
author = {Uri Onn and Pooja Singla},
journal= {arXiv preprint arXiv:1101.2738},
year = {2011}
}
Comments
Final version, to appear in JPAA, 14 pages