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- W2963009445 abstract "We study the exceptional theta correspondence for real groups obtained by restricting the minimal representation of the split exceptional group of the type <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=bold upper E Subscript n> <mml:semantics> <mml:msub> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=bold>E</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msub> <mml:annotation encoding=application/x-tex>mathbf E_n</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, to a split dual pair where one member is the exceptional group of the type <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=bold upper G 2> <mml:semantics> <mml:msub> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=bold>G</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> <mml:annotation encoding=application/x-tex>mathbf {G}_2</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. We prove that the correspondence gives a bijection between spherical representations if <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=n equals 6 comma 7> <mml:semantics> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:mn>6</mml:mn> <mml:mo>,</mml:mo> <mml:mn>7</mml:mn> </mml:mrow> <mml:annotation encoding=application/x-tex>n=6,7</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, and a slightly weaker statement if <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=n equals 8> <mml:semantics> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:mn>8</mml:mn> </mml:mrow> <mml:annotation encoding=application/x-tex>n=8</mml:annotation> </mml:semantics> </mml:math> </inline-formula>." @default.
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- W2963009445 date "2018-08-24" @default.
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- W2963009445 title "Duality for spherical representations in exceptional theta correspondences" @default.
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- W2963009445 doi "https://doi.org/10.1090/tran/7471" @default.
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