Abstract
We decompose the exterior and symmetric square of the reflection representation of the groups GL ( n ) and SO + ( 2 m ) over a finite field of odd characteristic. As a byproduct of the method, we confirm a new case ( r = 2 , m ⩾ 4 ) of a conjecture of Aubert, Michel and Rouquier describing the unipotent part of the Howe correspondence between Sp ( 2 r ) and SO + ( 2 m ) .
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