Uniformly Bounded Multiplicities in the Branching Problem and D-modules
Time: 2022-08-19
Published By: He Liu
Speaker(s): Masatoshi Kitagawa (Waseda University)
Time: 14:00-15:00 August 24, 2022
Venue: Online
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 D-modules (and 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.
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