Small principal series and exceptional duality for two simply laced exceptional groups

Salmasian, Hadi

doi:10.1090/S0002-9947-08-04530-3

Small principal series and exceptional duality for two simply laced exceptional groups
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Trans. Amer. Math. Soc. 361 (2009), 1925-1947 Request permission

Abstract:

We use the notion of rank defined in an earlier paper (2007) to introduce and study two correspondences between small irreducible unitary representations of the split real simple Lie groups of types $\mathbf E_n$, where $n\in \{6,7\}$, and two reductive classical groups. We show that these correspondences classify all of the unitary representations of rank two (in the sense of our earlier paper) of these exceptional groups. We study our correspondences for a specific family of degenerate principal series representations in detail.

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