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1962•Russian Mathematical SurveysOpen access

UNITARY REPRESENTATIONS OF NILPOTENT LIE GROUPS

A. A. Kirillov

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Abstract

CONTENTS Introduction § 1. Induced representations § 2. Representations of Lie algebras and infinitesimal group rings § 3. A special nilpotent group N § 4. Nilpotent Lie groups with one-dimensional centre § 5. Description of the representations of nilpotent Lie groups § 6. Orbits and representations § 7. Representations of the group ring § 8. Some generalizations and unsolved problems § 9. Examples References

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CONTENTS Introduction § 1. Induced representations § 2. Representations of Lie algebras and infinitesimal group rings § 3. A special nilpotent group N § 4. Nilpotent Lie groups with one-dimensional centre § 5. Description of the representations of nilpotent Lie groups § 6. Orbits and representations § 7. Representations of the group ring § 8. Some generalizations and unsolved problems § 9. Examples References

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CONTENTS Introduction § 1. Induced representations § 2. Representations of Lie algebras and infinitesimal group rings § 3. A special nilpotent group N § 4. Nilpotent Lie groups with one-dimensional centre § 5. Description of the representations of nilpotent Lie groups § 6. Orbits and representations § 7. Representations of the group ring § 8. Some generalizations and unsolved problems § 9. Examples References

Key concepts: Mathematics, Nilpotent, Representation of a Lie group, Central series, Pure mathematics, Nilpotent group, Infinitesimal, Lie group

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