A rigidity result for dimension data
Group Theory
2013-03-05 v1 Representation Theory
Abstract
The dimension datum of a closed subgroup of a compact Lie group is a sequence by assigning the invariant dimension of each irreducible representation restricting to the subgroup. We prove that any sequence of dimension data contains a converging sequence with limit the dimension datum of a subgroup interrelated to subgroups giving this sequence. This rigidity has an immediate corollary that the space of dimension data of closed subgroups in a given compact Lie group is sequentially compact.
Keywords
Cite
@article{arxiv.1303.0812,
title = {A rigidity result for dimension data},
author = {Jun Yu},
journal= {arXiv preprint arXiv:1303.0812},
year = {2013}
}