Full computation of Howe duality restrictions over finite fields yields recursive irrep constructions for symplectic and orthogonal groups plus proofs of rank and exhaustion conjectures for type C.
Prasad, Weil representation, Howe duality, and the theta correspondence, In: Theta Functions: From the Classical to the Modern, CRM Proc
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Constructs the type I Howe duality correspondence in the two stable ranges over finite fields as the first paper in a series.
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Howe duality over finite fields III: Full computation and the Gurevich-Howe conjectures
Full computation of Howe duality restrictions over finite fields yields recursive irrep constructions for symplectic and orthogonal groups plus proofs of rank and exhaustion conjectures for type C.
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Howe duality over finite fields I: The two stable ranges
Constructs the type I Howe duality correspondence in the two stable ranges over finite fields as the first paper in a series.