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In this short note we expand on recent results on the degenerate principle series   $I(s,\chi )$   of classical groups associated to   $s\in \mathbb{C}$   and a quadratic character   $\chi $  . In particular, we strengthen the result for   $s\in \mathbb{R}_{\ge 0}$  , which allows us to give as a corollary a new proof of the Howe duality conjecture for symplectic-orthogonal and unitary pairs.

A Note on the Howe Duality Conjecture for Symplectic-Orthogonal and Unitary Pairs