On double coset decompositions of real reductive groups for reductive absolutely spherical subgroups. (English) Zbl 1493.22017
Baklouti, Ali (ed.) et al., Geometric and harmonic analysis on homogeneous spaces and applications. TJC 2019, Djerba, Selected papers based on the presentations at the 6th Tunisian-Japanese conference. In honor of Professor Takaaki Nomura. Tunisia, December 15–19, 2019. Cham: Springer. Springer Proc. Math. Stat. 366, 229-267 (2021).
In the paper under review the author studies the double coset decomposition \(H\backslash G/L\) of a real reductive Lie group \(G\) with respect to reductive absolutely spherical subgroups \(H\) and \(L\). By the induction combined with computations for some minimal cases and reductions of some double coset spaces to more smaller groups, the author describes generic double cosets for reductive absolutely spherical pairs with some exceptions. The exceptional cases to which the argument of this article cannot be applied arise from some factorizations of type \(D_4\)-groups.
For the entire collection see [Zbl 1477.43001].
For the entire collection see [Zbl 1477.43001].
Reviewer: Sergei S. Platonov (Petrozavodsk)
MSC:
| 22E46 | Semisimple Lie groups and their representations |
| 22F30 | Homogeneous spaces |
| 53C30 | Differential geometry of homogeneous manifolds |
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