TEMPERED SPECTRAL TRANSFER IN THE TWISTED ENDOSCOPY OF REAL GROUPS
2014 ◽
Vol 15
(3)
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pp. 569-612
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Keyword(s):
Suppose that $G$ is a connected reductive algebraic group defined over $\mathbf{R}$, $G(\mathbf{R})$ is its group of real points, ${\it\theta}$ is an automorphism of $G$, and ${\it\omega}$ is a quasicharacter of $G(\mathbf{R})$. Kottwitz and Shelstad defined endoscopic data associated to $(G,{\it\theta},{\it\omega})$, and conjectured a matching of orbital integrals between functions on $G(\mathbf{R})$ and its endoscopic groups. This matching has been proved by Shelstad, and it yields a dual map on stable distributions. We express the values of this dual map on stable tempered characters as a linear combination of twisted characters, under some additional hypotheses on $G$ and ${\it\theta}$.
1971 ◽
Vol 12
(1)
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pp. 1-14
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2019 ◽
Vol 2019
(754)
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pp. 1-15
1982 ◽
Vol 92
(1)
◽
pp. 65-72
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2013 ◽
Vol 13
(2)
◽
pp. 199-248
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Keyword(s):
2014 ◽
Vol 14
(3)
◽
pp. 493-575
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