Geodesic
Compatibility of theta lifts and tempered condition
Canadian mathematical bulletin, Tome 67 (2024) no. 1, pp. 60-73

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DOI

In 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.
DOI : 10.4153/S0008439523000516
Mots-clés : Tempered representations, theta correspondence, metaplectic groups, Weil representations 
Li, Zhe; Wang, Shanwen. Compatibility of theta lifts and tempered condition. Canadian mathematical bulletin, Tome 67 (2024) no. 1, pp. 60-73. doi: 10.4153/S0008439523000516
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