Abstract
AbstractIn this note, assuming the nonvanishing result of explicit theta correspondence for the symplectic–orthogonal dual pair over quaternion algebra $\mathbb {H}$ , we show that, for metapletic–orthogonal dual pair over $\mathbb {R}$ and the symplectic–orthogonal dual pair over quaternion algebra $\mathbb {H}$ , the theta correspondence is compatible with tempered condition by directly estimating the matrix coefficients, without using the classification theorem.
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