Mots-clés : algebraic group
@article{SM_2014_205_9_a0,
author = {R. S. Avdeev and A. V. Petukhov},
title = {Spherical actions on flag varieties},
journal = {Sbornik. Mathematics},
pages = {1223--1263},
year = {2014},
volume = {205},
number = {9},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2014_205_9_a0/}
}
R. S. Avdeev; A. V. Petukhov. Spherical actions on flag varieties. Sbornik. Mathematics, Tome 205 (2014) no. 9, pp. 1223-1263. http://geodesic.mathdoc.fr/item/SM_2014_205_9_a0/
[1] D. A. Timashev, Homogeneous spaces and equivariant embeddings, Encyclopaedia Math. Sci., 138, Springer, Heidelberg, 2011, xxii+253 pp. | DOI | MR | Zbl
[2] A. L. Onischik, “Otnosheniya vklyucheniya mezhdu tranzitivnymi kompaktnymi gruppami preobrazovanii”, Tr. MMO, 11, GIFML, M., 1962, 199–242 | MR | Zbl
[3] M. Demazure, “Automorphismes et déformations des variétés de Borel”, Invent. Math., 39:2 (1977), 179–186 | DOI | MR | Zbl
[4] P. Littelmann, “On spherical double cones”, J. Algebra, 166:1 (1994), 142–157 | DOI | MR | Zbl
[5] P. Magyar, J. Weyman, A. Zelevinsky, “Multiple flag varieties of finite type”, Adv. Math., 141:1 (1999), 97–118 | DOI | MR | Zbl
[6] P. Magyar, J. Weyman, A. Zelevinsky, “Symplectic multiple flag varieties of finite type”, J. Algebra, 230:1 (2000), 245–265 | DOI | MR | Zbl
[7] J. R. Stembridge, “Multiplicity-free products and restrictions of Weyl characters”, Represent. Theory, 7 (2003), 404–439 (electronic) | DOI | MR | Zbl
[8] X. He, K. Nishiyama, H. Ochiai, Y. Oshima, “On orbits in double flag varieties for symmetric pairs”, Transform. Groups, 18:4 (2013), 1091–1136 | DOI | MR | Zbl
[9] B. Niemann, Spherical affine cones in exceptional cases and related branching rules, 2011, arXiv: 1111.3823
[10] R. W. Richardson, Jr., “Conjugacy classes in parabolic subgroups of semisimple algebraic groups”, Bull. London Math. Soc., 6:1 (1974), 21–24 | DOI | MR | Zbl
[11] I. V. Losev, “Algebraic Hamiltonian actions”, Math. Z., 263:3 (2009), 685–723 | DOI | MR | Zbl
[12] D. H. Collingwood, W. M. McGovern, Nilpotent orbits in semisimple Lie algebras, Van Nostrand Reinhold Math. Ser., Van Nostrand Reinhold Co., New York, 1993, xiv+186 pp. | MR | Zbl
[13] V. G. Kac, “Some remarks on nilpotent orbits”, J. Algebra, 64:1 (1980), 190–213 | DOI | MR | Zbl
[14] C. Benson, G. Ratcliff, “A classification of multiplicity free actions”, J. Algebra, 181:1 (1996), 152–186 | DOI | MR | Zbl
[15] A. S. Leahy, “A classification of multiplicity free representations”, J. Lie Theory, 8:2 (1998), 367–391 | MR | Zbl
[16] F. Knop, “Some remarks on multipicity free spaces”, Representation theories and algebraic geometry (Montreal, PQ, 1997), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 514, Kluwer Acad. Publ., Dordrecht, 1998, 301–317 | MR | Zbl
[17] A. V. Petukhov, “Bounded reductive subalgebras of $\mathfrak{sl}_n$”, Transform. Groups, 16:4 (2011), 1173–1182 | DOI | MR | Zbl
[18] E. B. Vinberg, “Commutative homogeneous spaces and co-isotropic symplectic actions”, Russian Math. Surveys, 56:1 (2001), 1–60 | DOI | DOI | MR | Zbl
[19] F. Knop, “Weylgruppe und Momentabbildung”, Invent. Math., 99:1 (1990), 1–23 | DOI | MR | Zbl
[20] R. Brylinski, B. Kostant, “Nilpotent orbits, normality, and Hamiltonian group actions”, J. Amer. Math. Soc., 7:2 (1994), 269–298 | MR | Zbl
[21] V. L. Popov, E. B. Vinberg, “Invariant theory”, Algebraic geometry. IV. Linear algebraic groups, invariant theory, Encyclopaedia Math. Sci., 55, Springer-Verlag, Berlin, 1994, 123–284 | DOI | MR | MR | Zbl | Zbl
[22] H. Kraft, C. Procesi, “Closures of conjugacy classes of matrices are normal”, Invent. Math., 53:3 (1979), 227–247 | DOI | MR | Zbl
[23] D. S. Johnston, R. W. Richardson, “Conjugacy classes in parabolic subgroups of semisimple algebraic groups. II”, Bull. London Math. Soc., 9:3 (1977), 245–250 | DOI | MR | Zbl
[24] H. Kraft, “Parametrisierung von Konjugationsklassen in $\mathfrak{sl}_n$”, Math. Ann., 234:3 (1978), 209–220 | DOI | MR | Zbl
[25] A. G. Èlashvili, “Stationary subalgebras of points of the common state for irreducible linear Lie groups”, Funct. Anal. Appl., 6:2 (1972), 139–148 | DOI | MR | Zbl
[26] D. I. Panyushev, “Complexity and rank of homogeneous spaces”, Geom. Dedicata, 34:3 (1990), 249–269 | DOI | MR | Zbl
[27] M. Sato, T. Kimura, “A classification of irreducible prehomogeneous vector spaces and their relative invariants”, Nagoya Math. J., 65 (1977), 1–155 | MR | Zbl
[28] M. Krämer, “Sphärische Untergruppen in kompakten zusammenhängenden Liegruppen”, Compositio Math., 38:2 (1979), 129–153 | MR | Zbl