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- W3045806594 abstract "In this article we consider the set<inline-formula content-type=math/mathml><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper G><mml:semantics><mml:mi>G</mml:mi><mml:annotation encoding=application/x-tex>G</mml:annotation></mml:semantics></mml:math></inline-formula>of rational points of a quaternionic form of a symplectic or an orthogonal group defined over a non-Archimedean local field of odd residue characteristic. We construct all full self-dual semisimple characters for<inline-formula content-type=math/mathml><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper G><mml:semantics><mml:mi>G</mml:mi><mml:annotation encoding=application/x-tex>G</mml:annotation></mml:semantics></mml:math></inline-formula>and we classify their intertwining classes using endo-parameters. We compute the set of intertwiners between self-dual semisimple characters, and prove an intertwining and conjugacy theorem. Finally we count all<inline-formula content-type=math/mathml><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper G><mml:semantics><mml:mi>G</mml:mi><mml:annotation encoding=application/x-tex>G</mml:annotation></mml:semantics></mml:math></inline-formula>-intertwining classes of full self-dual semisimple characters which lift to the same<inline-formula content-type=math/mathml><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper G overTilde><mml:semantics><mml:mrow class=MJX-TeXAtom-ORD><mml:mover><mml:mi>G</mml:mi><mml:mo stretchy=false>~<!-- ~ --></mml:mo></mml:mover></mml:mrow><mml:annotation encoding=application/x-tex>tilde {G}</mml:annotation></mml:semantics></mml:math></inline-formula>-intertwining class of a full semisimple character for the ambient general linear group<inline-formula content-type=math/mathml><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper G overTilde><mml:semantics><mml:mrow class=MJX-TeXAtom-ORD><mml:mover><mml:mi>G</mml:mi><mml:mo stretchy=false>~<!-- ~ --></mml:mo></mml:mover></mml:mrow><mml:annotation encoding=application/x-tex>tilde {G}</mml:annotation></mml:semantics></mml:math></inline-formula>for<inline-formula content-type=math/mathml><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper G><mml:semantics><mml:mi>G</mml:mi><mml:annotation encoding=application/x-tex>G</mml:annotation></mml:semantics></mml:math></inline-formula>." @default.
- W3045806594 created "2020-08-03" @default.
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- W3045806594 date "2020-07-29" @default.
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- W3045806594 title "Semisimple characters for inner forms II: Quaternionic forms of 𝑝-adic classical groups (𝑝 odd)" @default.
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- W3045806594 doi "https://doi.org/10.1090/ert/544" @default.
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