A cell filtration of mixed tensor space
Representation Theory
2014-08-29 v1
Abstract
We construct a cellular basis of the walled Brauer algebra which has similar properties as the Murphy basis of the group algebra of the symmetric group. In particular, the restriction of a cell module to a certain subalgebra can be easily described via this basis. Furthermore, the mixed tensor space possesses a filtration by cell modules -- although not by cell modules of the walled Brauer algebra itself, but by cell modules of its image in the algebra of endomorphisms of mixed tensor space.
Cite
@article{arxiv.1408.6720,
title = {A cell filtration of mixed tensor space},
author = {Friederike Stoll and Mathias Werth},
journal= {arXiv preprint arXiv:1408.6720},
year = {2014}
}