A Compactness Result for Dimension Datum

作者：Yu Jun^*

来源：International Mathematics Research Notices, 2015, 2015(19): 9438-9449.

DOI：10.1093/imrn/rnu229

Given a compact Lie group G and a closed subgroup H, the dimension datum of H is the map DH : (G) over cap -> Z which assigns to each irreducible complex linear representation W of G the dimension of W-H, the subspace of H- invariant vectors. We prove that as a subspace of Z((G) over cap) the set consisting of dimension data of closed subgroups of G is compact. We obtain new proofs of some previously known finiteness and rigidity results and we give an application to spectral geometry.

• 出版日期2015