Frobenius reciprocity and extensions of nilpotent Lie groups

Fox, Jeffrey

doi:10.1090/S0002-9947-1986-0857436-1

Frobenius reciprocity and extensions of nilpotent Lie groups
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Trans. Amer. Math. Soc. 298 (1986), 123-144 Request permission

Abstract:

In $\S 1$ we use ${C^\infty }$-vector methods, essentially Frobenius reciprocity, to derive the Howe-Richardson multiplicity formula for compact nilmanifolds. In $\S 2$ 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 $\S 3$ we give an application of the previous results to obtain a reduction formula for solvable Lie groups.

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