Finite multiplicity theorems for induction and restriction

By Toshiyuki Kobayashi, T. Oshima. 2011

114 citations recorded by the source corpus.

Abstract We find upper and lower bounds of the multiplicities of irreducible admissible representations π of a semisimple Lie group G occurring in the induced representations Ind H G τ from irreducible representations τ of a closed subgroup H. As corollaries, we establish geometric criteria for finiteness of the dimension of Hom G ( π , Ind H G τ ) (induction) and of Hom H ( π | H , τ ) (restriction) by means of the real flag variety G / P , and discover that uniform boundedness property of these multiplicities is independent of real forms and characterized by means of the complex flag variety.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/81e3b2a5c53672b3952e81e490ca79c1cf2c46c8

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Discrete Mathematics and Combinatorics

1. T. Matsuki
2. Toshiyuki Kobayashi

In Geometry and Topology

1. T. Matsuki
2. Toshiyuki Kobayashi
3. M. Pevzner

In Mathematical Physics

1. T. Matsuki
2. Toshiyuki Kobayashi
3. M. Pevzner

Citations in the corpus

• CLASSIFICATION OF FINITE-MULTIPLICITY SYMMETRIC PAIRS (2013, methodology): “Moreover, the bounded-multiplicity property (BM) depends only on the complexified Lie algebra (gC, hC), as was proved in [13].”