References
D. N. Akhiezer, Lie Group Actions in Complex Analysis, Vieweg, Braunschweig/Wiesbaden (1995).
N. Bourbaki, Groupes et algèbres de Lie, Ch. 7–8, Hermann, Paris (1977).
V. A. Bunegina and A. L. Onishchik, “Two families of flag supermanifolds,” Differ. Geom. Appl., 4, 329–360 (1994).
N. I. Ivanova, “On flag split supermanifolds,” in: Problems of the Theory of Groups and Homological Algebra [in Russian], Yaroslavl University (1998), pp. 115–128.
N. I. Ivanova, “On parabolic subalgebras of Lie superalgebras of classical type,” in: Modern Problems of Mathematics and Informatics [in Russian], 3, Yaroslavl University (2000), pp. 16–21.
N. I. Ivanova, “On parabolic subalgebras of the Lie superalgebras {ie3689-01},” in: Modern Problems of Mathematics and Informatics [in Russian], 4, Yaroslavl University (2001), pp. 18–24.
N. I. Ivanova, “Parabolic subalgebras of Lie superalgebras of classical type,” Problems of the Theory of Groups and Homological Algebra [in Russian], Yaroslavl University (2003), pp. 118–151.
N. I. Ivanova, “The systems of indecomposable roots of the Lie superalgebras {ie3689-02},” in: Modern Problems of Mathematics and Informatics [in Russian], 7, Yaroslavl University (2005), pp. 13–21.
V. G. Kac, “Lie superalgebras,” Adv. Math., 26, 8–96 (1977).
V. G. Kac, “Graded Lie superalgebras and Jordan superalgebras,” Commun. Algebra, 5, 1375–1400 (1977).
Yu. I. Manin, Topics in Noncommutative Geometry, Princeton Univ. Press, Princeton (1991).
Yu. I. Manin, Gauge Field Theory and Complex Geometry, Springer-Verlag, Berlin (1997).
A. L. Onishchik, “Transitive Lie superalgebras of vector fields,” Reports Dep. Math. Univ. Stockholm, 26, 1–21 (1987).
A. L. Onishchik, “Flag supermanifolds, their automorphisms and deformations,” in: Proc. Sophus Lie Memorial Conference, Oslo, 1992, Scand. Univ. Press, Oslo (1994), pp. 289–302.
A. L. Onishchik and O. V. Platonova, “Homogeneous supermanifolds associated with complex projective space, I,” Mat. Sb., 189, No. 2, 111–136 (1998)
A. L. Onishchik and E. B. Vinberg, Lie Groups and Algebraic Groups, Springer-Verlag, Berlin (1990).
I. Penkov, “Borel-Weil-Bott theory for classical Lie supergroups,” Sovr. Probl. Mat., 32, 71–124 (1988).
I. Penkov, “Characters of strongly generic irreducible Lie superalgebra representations,” Int. J. Math., 9, 331–366 (1998).
I. Penkov and V. Serganova, “Generic irreducible representations of finite-dimensional Lie superalgebras,” Int. J. Math., 5, 389–419 (1994).
M. Scheunert, The Theory of Lie Superalgebras. An Introduction, Lect. Notes Math., 716, Springer-Verlag, Berlin (1979).
A. A. Voronov and Yu. I. Manin, “Supercell decompositions of the superspaces of flags,” Sovr. Probl. Mat., 32, 27–70 (1988).
K. Yamaguchi, “Differential systems associated with simple graded Lie algebras,” Progr. Differ. Geom. Adv. Stud. Pure Math., 22, 413–494 (1993).
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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 20, Algebra, 2006.
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Ivanova, N.I., Onishchik, A.L. Parabolic subalgebras and gradings of reductive Lie superalgebras. J Math Sci 152, 1–60 (2008). https://doi.org/10.1007/s10958-008-9049-8
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DOI: https://doi.org/10.1007/s10958-008-9049-8