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\SL_3 dual pairs

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Abstract · v1

We study the exceptional theta correspondence for dual pairs of the form \SL_3\times G inside pp-adic groups of type EnE_n, n=6,7,8n=6,7,8. We establish Howe duality for lifts of all Whittaker-generic unitarizable representations of \SL_3. Our dual pair is in a see-saw relationship with a dual pair of the form G2×HG_2 \times H such that G/HG/H is a rank-two symmetric space. Using the theta correspondence for \SL_3 \times G, we prove a multiplicity-one result for HH-invariant functionals on representations of GG.

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