YAMASHITA Hiroshi Specially Appointed Professor


Department of Mathematics
Research Interest
Representation Theory
induced modules, invariant differential operators, irreducible admissible representations, nilpotent orbits, semisimple Lie groups/ Lie algebras

Research Activities

I am interested in infinite-dimensional representation theory of real reductive Lie groups. This is one of the most highly developed, central research areas in modern mathematics. It is connected to various other branches such as number theory, algebraic geometry, combinatorics, differential geometry, harmonic analysis, algebraic analysis, functional analysis, mathematical physics, differential equations, etc. I focus my attention to understand infinite-dimensional representations in relation to nilpotent orbits on Lie algebras, by studying geometric invariants and nice realization/model of such representations.

Selected Publications:


H. Yamashita, Embeddings of discrete series into induced representations of semisimple Lie groups, I, Japan. J. Math., 16 (1990), 31–95; II, J. Math. Kyoto Univ., 31 (1991), 543–571.

H. Yamashita, Cayley transform and generalized Whittaker models for irreducible highest weight modules, in: “Nilpotent orbits, associated cycles and Whittaker models for highest weight representations”, Ast\’erisque 273 (2001), 81–137.

(Books etc.)

平井武・山下博(共著),表現論入門セミナー:具体例から最先端に向かって,遊星社,2003, xi, 329p, ISBN4-7952-6898-3 (第II部:リー代数と表現論を執筆).

山下博述・阿部紀行記,簡約リー群の表現と冪零軌道東京大学数理科学レクチャーノート 3, 2008, iii, 77p.