On the spectrum of (𝑆𝑝𝑖𝑛(10,2),𝑆𝐿(2,ℝ)) in 𝔼_{7,3}

Du, Zhe

doi:10.1090/S0002-9939-2010-10664-0

On the spectrum of $(Spin(10,2),SL(2,\mathbb {R}))$ in $E_{7,3}$
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Proc. Amer. Math. Soc. 139 (2011), 757-768 Request permission

Abstract:

We give the complete description of the spectrum of $(Spin(10,2),SL(2,\mathbb {R}))$ in the minimal representation of $E_{7,3}$, and we find that it only consists of a discrete spectrum. This is interesting as both groups are noncompact. Also, most of the representations occurring in the spectrum are unitary representations with nonzero cohomology. The representations we obtained have different Hodge types from the representations we obtain from classical theta liftings.

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