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Kirillov models for distinguished representations

Published online by Cambridge University Press:  22 January 2016

Courtney Moen
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In the theory of automorphic forms on covering groups of the general linear group, a central role is played by certain local representations which have unique Whittaker models. A representation with this property is called distinguished. In the case of the 2-sheeted cover of GL2, these representations arise as the the local components of generalizations of the classical θ-function. They have been studied thoroughly in [GPS]. The Weil representation provides these representations with a very nice realization, and the local factors attached to these representations can be computed using this realization. It has been shown [KP] that only in the case of a certain 3-sheeted cover do we find other principal series of covering groups of GL2 which have a unique Whittaker model. It is natural to ask if these distinguished representations also have a realization analgous to the Weil representation.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 116 , December 1989 , pp. 89 - 110
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1989

References

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