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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Unipotent representations and reductive dual pairs over finite fields


Authors: Jeffrey Adams and Allen Moy
Journal: Trans. Amer. Math. Soc. 340 (1993), 309-321
MSC: Primary 20G05; Secondary 20C15, 20G40
DOI: https://doi.org/10.1090/S0002-9947-1993-1173855-4
MathSciNet review: 1173855
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Abstract: Consider the representation correspondence for a reductive dual pair $ ({G_1},{G_2})$ over a finite field. We consider the question of how the correspondence behaves for unipotent representations. In the special case of cuspidal unipotent representations, and a certain fundamental situation, that of "first occurrence", the representation correspondence takes a cuspidal unipotent representation of $ {G_1}$ to one of $ {G_2}$. This should serve as a fundamental case in studying the correspondence in general over both finite and local fields.


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DOI: https://doi.org/10.1090/S0002-9947-1993-1173855-4
Article copyright: © Copyright 1993 American Mathematical Society