English

Dirac series of $E_{7(-5)}$

Representation Theory 2022-09-23 v2

Abstract

Using the sharpened Helgason-Johnson bound, this paper classifies all the irreducible unitary representations with non-zero Dirac cohomology of E7(5)E_{7(-5)}. As an application, we find that the cancellation between the even part and the odd part of the Dirac cohomology continues to happen for certain unitary representations of E7(5)E_{7(-5)}. Assuming the infinitesimal character being integral, we further improve the Helgason-Johnson bound for E7(5)E_{7(-5)}. This should help people to understand (part of) the unitary dual of this group.

Cite

@article{arxiv.2205.11999,
  title  = {Dirac series of $E_{7(-5)}$},
  author = {Yi-Hao Ding and Chao-Ping Dong and Ping-Yuan Li},
  journal= {arXiv preprint arXiv:2205.11999},
  year   = {2022}
}

Comments

25 pages. arXiv admin note: text overlap with arXiv:2204.07902

R2 v1 2026-06-24T11:26:56.138Z