|
On solvable spherical subgroups of semisimple algebraic groups
Author:
R. S. Avdeev
Translated by:
E. Khukhro
Original publication:
Trudy Moskovskogo Matematicheskogo Obshchestva, tom 72 (2011), vypusk 1.
Journal:
Trans. Moscow Math. Soc. 2011, 1-44
MSC (2010):
Primary 20G07; Secondary 14M27, 14M17
Posted:
January 12, 2012
Full-text PDF
Abstract |
References |
Similar Articles |
Additional Information
Abstract: We develop a structure theory of connected solvable spherical subgroups in semisimple algebraic groups. Based on this theory, we obtain an explicit classification of all such subgroups up to conjugacy.
References
- 1.
M. Krämer, Sphärische Untergruppen in kompakten zusammenhängenden Liegruppen, Compositio Math. 38 (1979), no. 2, 129-153. MR 528837 (80f:22011)
- 2.
I. V. Mikityuk, Integrability of invariant Hamiltonian systems with homogeneous configuration spaces, Mat. Sb. 129 (1986), no. 4, 514-534; English transl., Math. USSR-Sb. 57 (1987), 527-546. MR 842398 (88e:58032)
- 3.
M. Brion, Classification des espaces homogènes sphériques, Compositio Math. 63 (1987), no. 2, 189-208. MR 906369 (89d:32068)
- 4.
O. S. Yakimova, Weakly symmetric spaces of semisimple Lie groups, Vestnik Moskov. Univ. Ser. I Mat. Mekh. 2002 (2002), no. 2, 57-60; English transl., Moscow Univ. Math. Bull. 57 (2002), no. 2, 37-40. MR 1934062 (2004b:53076)
- 5.
D. Luna, Sous-groupes sphériques résolubles, Prépublication de l'Institut Fourier, 1993, no. 241.
- 6.
D. Luna, Variétés sphériques de type
𝐴, Publ. Math. Inst. Hautes Études Sci. , posted on
(2001), no. 94, 161–226 (French). MR 1896179
(2003f:14056), http://dx.doi.org/10.1007/s10240-001-8194-0
- 7.
P. Bravi and G. Pezzini, Wonderful varieties of type
 and  , arXiv:0909.3771v1.
- 8.
S. Cupit-Foutou, Wonderful varieties: a geometrical realization, arXiv:0907.2852v3.
- 9.
R. Avdeev, On solvable spherical subgroups of semisimple algebraic groups, Oberwolfach Reports, 7 (2010), no. 2, 1105-1108.
- 10.
È. B. Vinberg and A. L. Onishchik, Seminar on Lie groups and algebraic groups, URSS, Moscow, 1995; English transl. of 1st ed., A. L. Onishchik and È. B. Vinberg, Lie groups and algebraic groups, Springer Series in Soviet Mathematics, Springer-Verlag, Berlin, 1990. MR 1403378 (97d:22001)
- 11.
Pierre-Louis Montagard, Une nouvelle propriété de
stabilité du pléthysme, Comment. Math. Helv.
71 (1996), no. 3, 475–505 (French). MR 1418950
(97m:20054), http://dx.doi.org/10.1007/BF02566432
- 12.
È. B. Vinberg, Commutative homogeneous spaces and co-isotropic
symplectic actions, Uspekhi Mat. Nauk 56 (2001),
no. 1(337), 3–62 (Russian, with Russian summary); English
transl., Russian Math. Surveys 56 (2001), no. 1,
1–60. MR
1845642 (2002f:53088), http://dx.doi.org/10.1070/rm2001v056n01ABEH000356
Similar Articles
Retrieve articles in Transactions of the Moscow Mathematical Society
with MSC (2010):
20G07,
14M27,
14M17
Retrieve articles in all journals
with MSC (2010):
20G07,
14M27,
14M17
Additional Information
R. S. Avdeev
Affiliation:
Moscow State University, Russia
Email:
suselr@yandex.ru
DOI:
http://dx.doi.org/10.1090/S0077-1554-2012-00192-7
PII:
S 0077-1554(2012)00192-7
Keywords:
Algebraic group,
homogeneous space,
spherical subgroup,
solvable subgroup
Posted:
January 12, 2012
Additional Notes:
This research was partially supported by the Russian Foundation for Basic Research (grant no. 09-01-00648-a).
Article copyright:
© Copyright 2012 American Mathematical Society
|
