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Totally real orbits in affine quotients of reductive groups
| Content Provider | Scilit |
|---|---|
| Author | Azad, H. Loeb, J. J. Qureshi, M. N. |
| Copyright Year | 1995 |
| Description | Let K be a compact connected Lie group and L a closed subgroup of K In [8] M. Lassalle proves that if K is semisimple and L is a symmetric subgroup of K then the holomorphy hull of any K-invariant domain in $K^{c}/L^{c}$ contains K/L. In [1] there is a similar result if L contains a maximal torus of K. The main group theoretic ingredient there was the characterization of K/L as the unique totally real K-orbit in $K^{c}/L^{c}$. On the other hand, Patrizio and Wong construct in [9] special exhaustion functions on the complexification of symmetric spaces K/L of rank 1 and find that the minimum value of their exhaustions is always achieved on K/L. By a lemma of Harvey and Wells [6] one knows that the set where a strictly plurisubharmonic (briefly s.p.s.h) function achieves its minimum is totally real. There is a related result in [2, Lemma 1.3] which states that if φ is any differentiable function on a complex manifold M then the form $dd^{c}$φ vanishes identically on any real submanifold N contained in the critical set of φ; in particular if φ is s.p.s.h then N must be totally real. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/D6C61F22572F10C7FF2CD67561ABF1BA/S0027763000005316a.pdf/div-class-title-totally-real-orbits-in-affine-quotients-of-reductive-groups-div.pdf |
| Ending Page | 92 |
| Page Count | 6 |
| Starting Page | 87 |
| ISSN | 00277630 |
| e-ISSN | 21526842 |
| DOI | 10.1017/s0027763000005316 |
| Journal | Nagoya Mathematical Journal |
| Volume Number | 139 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 1995-09-01 |
| Access Restriction | Open |
| Subject Keyword | Nagoya Mathematical Journal |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
