Classification of double flag varieties of complexity~0 and~1
Izvestiya. Mathematics , Tome 77 (2013) no. 5, pp. 998-1020.

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We obtain a classification of double flag varieties of complexity $0$ and $1$ and consider an application to the problem of decomposing tensor products of irreducible representations of semisimple Lie groups.
Keywords: semisimple Lie groups, double flag varieties, complexity, linear representations.
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E. V. Ponomareva. Classification of double flag varieties of complexity~0 and~1. Izvestiya. Mathematics , Tome 77 (2013) no. 5, pp. 998-1020. http://geodesic.mathdoc.fr/item/IM2_2013_77_5_a4/

[1] P. Littelmann, “On spherical double cones”, J. Algebra, 166:1 (1994), 142–157 | DOI | MR | Zbl

[2] J. R. Stembridge, “Multiplicity-free products and restrictions of Weyl character”, Represent. Theory, 7 (2003), 404–439 | DOI | MR | Zbl

[3] D. I. Panyushev, “Complexity and rank of double cones and tensor product decompositions”, Comment. Math. Helv., 68:3 (1993), 455–468 | DOI | MR | Zbl

[4] A. L. Onishchik, È. B. Vinberg, Lie groups and algebraic groups, Springer Ser. Soviet Math., Springer-Verlag, Berlin, 1990 | MR | MR | Zbl | Zbl

[5] F. Knop, H. Kraft, D. Luna, Th. Vust, “Local properties of algebraic group actions”, Algebraische Transformationsgruppen und Invariantentheorie, DMV Sem., 13, Birkhäuser, Basel, 1989, 63–75 | MR | Zbl

[6] W. Fulton, R. MacPherson, F. Sottile, B. Sturmfles, “Intersection theory on spherical varieties”, J. Algebraic Geom., 4:1 (1995), 181–193 | MR | Zbl

[7] M. Brion, “Groupe de Picard et nombres caractéristiques des variétés sphériques”, Duke Math. J., 58:2 (1989), 397–424 | DOI | MR | Zbl

[8] P. I. Katsylo, D. A. Timashev, “Natural differential operations on manifolds: an algebraic approach”, Sb. Math., 199:10 (2008), 1481–1503 | DOI | DOI | MR | Zbl

[9] D. A. Timashev, “Cartier divisors and geometry of normal $G$-varieties”, Transform. Groups, 5:2 (2000), 181–204 | DOI | MR | Zbl

[10] É. B. Vinberg, “Complexity of action of reductive groups”, Funct. Anal. Appl., 20:1 (1986), 1–11 | DOI | MR | Zbl

[11] D. I. Panyushev, “Complexity and rank of actions in invariant theory”, J. Math. Sci. (New York), 95:1 (1999), 1925–1985 | DOI | MR | Zbl