What question did this study set out to answer?

To explore the existence of irreducible representations with bounded multiplicity in simply connected non-compact semisimple Lie groups and identify which representations meet this criterion.

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March 29, 2026Open Access

Bounded Multiplicity Branching for Symmetric Pairs

Key Points

To explore the existence of irreducible representations with bounded multiplicity in simply connected non-compact semisimple Lie groups and identify which representations meet this criterion.
Proving properties of simply connected non-compact semisimple Lie groups
Analyzing the restriction of representations for symmetric pairs
Identifying conditions for bounded multiplicity
Any simply connected non-compact semisimple Lie group has an infinite-dimensional irreducible representation with bounded multiplicity
The results clarify which irreducible representations satisfy the bounded multiplicity property

Abstract

We prove that any simply connected non-compact semisimple Lie group G admits an infinite-dimensional irreducible representation with bounded multiplicity property of the restriction | G for all symmetric pairs (G, G ).We also discuss which irreducible representations satisfy the bounded multiplicity property.

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Cite This Study

T. Kobayashi (Sun,) studied this question.

synapsesocial.com/papers/69c8c15ade0f0f753b39bc25 https://doi.org/https://doi.org/10.5802/jolt.1285

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