Harmonically induced representations on nilpotent Lie groups and automorphic forms on nilmanifolds

Penney, Richard C.

doi:10.1090/S0002-9947-1980-0570782-9

Harmonically induced representations on nilpotent Lie groups and automorphic forms on nilmanifolds
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Trans. Amer. Math. Soc. 260 (1980), 123-145 Request permission

Abstract:

It is shown that the irreducible “discrete series” representations of certain nilpotent Lie groups may be realized in square integrable $\bar \partial$ cohomology spaces. This theory is applied to obtain a concept of automorphic forms on nilmanifolds which generalizes the niltheta functions of Cartier and Auslander-Tolimieri. We also use the automorphic cohomology to solve certain holomorphic difference equations on ${{\textbf {C}}^n}$.

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