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Frobenius reciprocity and extensions of nilpotent Lie groups


Author: Jeffrey Fox
Journal: Trans. Amer. Math. Soc. 298 (1986), 123-144
MSC: Primary 22E25; Secondary 22E27, 22E40, 22E45
DOI: https://doi.org/10.1090/S0002-9947-1986-0857436-1
MathSciNet review: 857436
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Abstract: In $ \S1$ we use $ {C^\infty }$-vector methods, essentially Frobenius reciprocity, to derive the Howe-Richardson multiplicity formula for compact nilmanifolds. In $ \S2$ we use Frobenius reciprocity to generalize and considerably simplify a reduction procedure developed by Howe for solvable groups to general extensions of nilpotent Lie groups. In $ \S3$ we give an application of the previous results to obtain a reduction formula for solvable Lie groups.


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DOI: https://doi.org/10.1090/S0002-9947-1986-0857436-1
Article copyright: © Copyright 1986 American Mathematical Society

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