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This article is cited in 7 scientific papers (total in 7 papers)
An analytic separation of series of representations for ${\rm SL}(2;\mathbb R)$
S. G. Gindikin Rutgers, The State University of New Jersey, Department of Mathematics
Abstract:
For the group ${\rm SL}(2;\mathbb R)$, holomorphic wave fronts of the projections on different series of representations are contained in some disjoint cones. These cones are convex for holomorphic and antiholomorphic series, which corresponds to the well-known fact that these projections can be extended holomorphically to some Stein tubes in ${\rm SL}(2;\mathbb C)$. For the continuous series, the cone is not convex, and the projections are boundary values of 1-dimensional $\bar\partial$-cohomology in a non-Stein tube.
Key words and phrases:
ntegral geometry, horospherical transform, series of representations, $\bar\partial$-cohomology, holomorphic wave front.
Received: April 16, 2002
Citation:
S. G. Gindikin, “An analytic separation of series of representations for ${\rm SL}(2;\mathbb R)$”, Mosc. Math. J., 2:4 (2002), 635–645
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https://www.mathnet.ru/eng/mmj66 https://www.mathnet.ru/eng/mmj/v2/i4/p635
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Abstract page: | 285 | References: | 79 |
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