Dirac series of $E_{7(7)}$
Representation Theory
2024-12-20 v2
Abstract
This paper classifies all the Dirac series (that is, irreducible unitary representations having non-zero Dirac cohomology) of . Enhancing the Helgason-Johnson bound in 1969 for the group is one key ingredient. Our calculation partially supports Vogan's fundamental parallelepiped (FPP) conjecture. As applications, when passing to Dirac index, we continue to find cancellation between the even part and the odd part of Dirac cohomology. Moreover, for the first time, we find Dirac series whose spin lowest -types have multiplicities.
Cite
@article{arxiv.2210.15833,
title = {Dirac series of $E_{7(7)}$},
author = {Yi-Hao Ding and Chao-Ping Dong and Lin Wei},
journal= {arXiv preprint arXiv:2210.15833},
year = {2024}
}
Comments
25 pages, accepted by Israel J Math. arXiv admin note: text overlap with arXiv:2205.11999