Abstract
The main purpose of this section is to fix notation. We refer to Knop (The Luna-Vust theory of spherical embeddings. In: Proceedings of the Hyderabad conference on algebraic groups, Hyderabad, 1989, pp 225–249. Manoj Prakashan, Madras, 1991) for a detailed treatment.
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References
Ash, A., Mumford, D., Rapoport, M., Tai, Y.S.: Smooth Compactifications of Locally Symmetric Varieties, 2nd edn. Cambridge Mathematical Library. Cambridge University Press, Cambridge (2010). http://dx.doi.org/10.1017/CBO9780511674693. With the collaboration of Peter Scholze
Benoist, Y., Oh, H.: Polar decomposition for p-adic symmetric spaces. Int. Math. Res. Not. IMRN 2007(24), 20 (2007). Art. ID rnm 121. http://dx.doi.org/10.1093/imrn/rnm121
Flensted-Jensen, M.: Spherical functions of a real semisimple Lie group. A method of reduction to the complex case. J. Funct. Anal. 30(1), 106–146 (1978). http://dx.doi.org/10.1016/0022-1236(78)90058-7
Kimura, T.: Introduction to Prehomogeneous Vector Spaces. Translations of Mathematical Monographs, vol. 215. American Mathematical Society, Providence (2003). Translated from the 1998 Japanese original by Makoto Nagura and Tsuyoshi Niitani and revised by the author
Knop, F.: The Luna-Vust theory of spherical embeddings. In: Proceedings of the Hyderabad Conference on Algebraic Groups (Hyderabad, 1989), pp. 225–249. Manoj Prakashan, Madras (1991)
Knop, F., Krötz, B., Sayag, E., Schlichtkrull, H.: Simple compactifications and polar decomposition of homogeneous real spherical spaces. Sel. Math. (N.S.) 21(3), 1071–1097 (2015). http://dx.doi.org/10.1007/s00029-014-0174-6
Sakellaridis, Y.: On the unramified spectrum of spherical varieties over p-adic fields. Compos. Math. 144(4), 978–1016 (2008). http://dx.doi.org/10.1112/S0010437X08003485
Sakellaridis, Y.: Spherical varieties and integral representations of L-functions. Algebra Number Theory 6(4), 611–667 (2012). http://dx.doi.org/10.2140/ant.2012.6.611
Sakellaridis, Y., Venkatesh, A.: Periods and Harmonic Analysis on Spherical Varieties. Astérisque, vol. 396, pp. viii+360. Mathematical Society of France, Paris (2017)
Shafarevich, I.R. (ed.): Algebraic Geometry IV. Encyclopaedia of Mathematical Sciences, vol. 55. Springer, Berlin (1994). http://dx.doi.org/10.1007/978-3-662-03073-8. Linear algebraic groups. Invariant theory, A translation of ıt Algebraic geometry. 4 (Russian), Akad. Nauk SSSR Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1989 [ MR1100483 (91k:14001)]. Translation edited by A.N. Parshin and I.R. Shafarevich
Timashev, D.A.: Homogeneous Spaces and Equivariant Embeddings. Encyclopaedia of Mathematical Sciences. Invariant Theory and Algebraic Transformation Groups, 8, vol. 138. Springer, Heidelberg (2011). http://dx.doi.org/10.1007/978-3-642-18399-7
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Li, WW. (2018). Geometric Background. In: Zeta Integrals, Schwartz Spaces and Local Functional Equations. Lecture Notes in Mathematics, vol 2228. Springer, Cham. https://doi.org/10.1007/978-3-030-01288-5_2
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