Uniformly bounded multiplicities in the branching problem and D-modules

Abstract: In the representation theory of real reductive Lie groups, several finiteness results of lengths and multiplicities are known and fundamental. The Harish-Chandra admissibility theorem and the finiteness of the length of Verma modules and principal series representations are typical examples.

More precisely, such multiplicities and lengths are bounded on some parameter sets. T. Oshima and T. Kobayashi ('13 adv. math.) gave a criterion on which branching laws have (uniformly) bounded multiplicities.

In arXiv:2109.05556, I defined uniform boundedness of a family of $\mathscr{D}$-modules (and $\mathfrak{g}$-modules) to treat the boundedness properties uniformly. I will talk about its definition and applications. In particular, I will give a necessary and sufficient condition on uniform boundedness of multiplicities in the branching problem of real reductive Lie groups.

algebraic geometrynumber theoryrepresentation theory

Audience: researchers in the topic

Comments: Zoom Number: 949 6559 4176

Zoom password: 071166

---

POINTS - Peking Online International Number Theory Seminar

Series comments: Description: Seminar on number theory and related topics

This seminar series is sponsored by the Beijing International Center of Mathematical Research (BICMR) and the School of Mathematical Sciences of Peking University.

The conference number and password are available on the external website. See also the announcements on bicmr.pku.edu.cn

---