HOMOGENEOUS SPHERICAL DATA OF ORBITS IN SPHERICAL EMBEDDINGS
详细信息 查看全文
- 作者：GIULIANO GAGLIARDI ; JOHANNES HOFSCHEIER
- 刊名：Transformation Groups
- 出版年：2015
- 出版时间：March 2015
- 年：2015
- 卷：20
- 期：1
- 页码：83-98
- 全文大小：271 KB
- 参考文献：1. P. Bravi, D. Luna, / An introduction to wonderful varieties with many examples of type F4, J. Algebra 329 (2011), 4-1.
2. M. Brion, F. Pauer, / Valuations des espaces homogènes sphériques, Comment. Math. Helv. 62 (1987), no. 2, 265-85.
3. M. Brion, / Groupe de Picard et nombres caractéristiques des variétés sphériques, Duke Math. J. 58 (1989), no. 2, 397-24.
4. M. Brion, / Vers une généralisation des espaces symétriques, J. Algebra 134 (1990), no. 1, 115-43.
5. D. A. Cox, J. B. Little, H. K. Schenck, / Toric Varieties, Graduate Studies in Mathematics, Vol. 124, American Mathematical Society, Providence, RI, 2011.
6. A. Foschi, / Variétés magnifiques et polytopes moment, PhD thesis, Université de Grenoble I, 1998.
7. F. Knop, H. Kraft, D. Luna, Th. Vust, / Local properties of algebraic group actions, in: / Algebraische Transformationsgruppen und Invariantentheorie, DMV Sem., Vol. 13, Birkh?user, Basel, 1989, pp. 63-5.
8. F. Knop, / The Luna-Vust theory of spherical embeddings, in: / Proceedings of the Hyderabad Conference on Algebraic Groups (Hyderabad, 1989), Manoj Prakashan, Madras, 1991, pp. 225-49.
9. I. V. Losev, / Uniqueness property for spherical homogeneous spaces, Duke Math. J. 147 (2009), no. 2, 315-43.
10. D. Luna, / Grosses cellules pour les variétés sphériques, in: / Algebraic groups and Lie groups, Austral. Math. Soc. Lect. Ser., Vol. 9, Cambridge Univ. Press, Cambridge, 1997, pp. 267-80.
11. D. Luna, / Variétés sphériques de type A, Publ. Math. Inst. Hautes études Sci. 94 (2001), 161-26.
12. D. Luna, Th. Vust, / Plongements d’espaces homogènes, Comment. Math. Helv. 58 (1983), no. 2, 186-45.
13. D. A. Timashev, / Homogeneous Spaces and Equivariant Embeddings, Encyclopaedia of Mathematical Sciences, Vol. 138, Subseries / Invariant Theory and Algebraic Transformation Groups, Vol. 8, Springer, Heidelberg, 2011. - 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Topological Groups and Lie Groups
Algebra - 出版者：Birkh盲user Boston
- ISSN：1531-586X
文摘
Let G be a connected reductive complex algebraic group. Luna assigned to any spherical homogeneous space G/H a combinatorial object called a homogeneous spherical datum. By a theorem of Losev, this object uniquely determines G/H up to G-equivariant isomorphism. In this paper, we determine the homogeneous spherical datum of a G-orbit X 0 in a spherical embedding G/H ?X. As an application, we obtain a description of the colored fan associated to the spherical embedding X 0 ? \( \overline{X_0} \) .