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This article is cited in 29 scientific papers (total in 29 papers)
Representations of pseudo-orthogonal groups associated with a cone
V. F. Molchanov
Abstract:
We study representations of the group $SO_0(p,q)$, $p>1$, $q>1$, in the spaces $D_\chi$, $\chi=(\sigma,\varepsilon)$ ($\sigma$ is a complex number; $\varepsilon=0$ or 1), of $C^\infty$-functions $\varphi(x)$ on the cone $-x_1^2-\dots-x_p^2+x_{p+1}^2+\dots+x_{p+q}^2=0$, $x\ne0$, of homogeneous degree $\sigma$ and parity $\varepsilon$: $\varphi(tx)=|t|^\sigma{\operatorname{sign}}^\varepsilon t\cdot\varphi(x)$. We consider the structure of the invariant subspaces, irreducibility, the operators which commute with the group (the intertwining operators), invariant Hermitian forms, and unitarity.
Figures: 1.
Bibliography: 12 titles.
Received: 18.03.1969
Citation:
V. F. Molchanov, “Representations of pseudo-orthogonal groups associated with a cone”, Math. USSR-Sb., 10:3 (1970), 333–347
Linking options:
https://www.mathnet.ru/eng/sm3378https://doi.org/10.1070/SM1970v010n03ABEH002158 https://www.mathnet.ru/eng/sm/v123/i3/p358
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