Abstract

Let ( G ′ , G ) be one of the following complex dual pairs: ( O ( m , C ) , Sp ( 2 n , C ) ) , ( GL ( m , C ) , GL ( 2 n , C ) ) , ( Sp ( 2 m , C ) , O ( 4 n , C ) ) . We determine the relationship between the space of G ′ -coinvariants and certain degenerate principal series representations of G. We also show that the space of G ′ -invariant distributions is generated by the Dirac distribution as a G-representation.

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