no. 2
Spherical varieties and Wahl’s conjecture
[Variétés sphériques et conjecture de Wahl]
Perrin, Nicolas1
1 Heinrich-Heine-Universität Mathematisches Institut Universitätsstr. 1 40225 Düsseldorf (Germany)
Annales de l'Institut Fourier, Tome 64 (2014) no. 2, pp. 739-751.

En utilisant les variétés sphériques, nous donnons, en toute caractéristique impaire, une preuve courte et uniforme de la conjecture de Wahl pour les variétés homogènes cominuscules.

Using the theory of spherical varieties, we give a type independent very short proof of Wahl’s conjecture for cominuscule homogeneous varieties for all primes different from 2.

DOI : 10.5802/aif.2864
Classification : 14M27, 14M15, 20G10
Keywords: Frobenius splitting, spherical varieties, Wahl’s conjecture
Mot clés : scindage de Frobenius, variétés sphériques, conjecture de Wahl

Perrin, Nicolas 1

1 Heinrich-Heine-Universität Mathematisches Institut Universitätsstr. 1 40225 Düsseldorf (Germany) 
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Perrin, Nicolas. Spherical varieties and Wahl’s conjecture. Annales de l'Institut Fourier, Tome 64 (2014) no. 2, pp. 739-751. doi : 10.5802/aif.2864. https://aif.centre-mersenne.org/articles/10.5802/aif.2864/

[1] Achinger, P.; Perrin, N. On spherical multiple flags (2013) (Preprint arXiv:1307.7236)

[2] Bourbaki, N. Groupes et algèbres de Lie, Hermann, Paris, 1954 | Zbl

[3] Brion, M.; Inamdar, S. P. Frobenius splitting of spherical varieties, Algebraic groups and their generalizations: classical methods (University Park, PA, 1991) (Proc. Sympos. Pure Math.), Volume 56, Amer. Math. Soc., Providence, RI, 1994, pp. 207-218 | MR | Zbl

[4] Brion, Michel; Kumar, Shrawan Frobenius splitting methods in geometry and representation theory, Progress in Mathematics, 231, Birkhäuser, Boston, MA, 2005, pp. x+250 | MR | Zbl

[5] Brown, J.; Lakshmibai, V. Wahl’s conjecture for a minuscule G/P, Proc. Indian Acad. Sci. Math. Sci., Volume 119 (2009) no. 5, pp. 571-592 | DOI | MR | Zbl

[6] De Concini, C.; Springer, T. A. Compactification of symmetric varieties, Transform. Groups, Volume 4 (1999) no. 2-3, pp. 273-300 (Dedicated to the memory of Claude Chevalley) | DOI | MR | Zbl

[7] Donkin, Stephen Invariants of unipotent radicals, Math. Z., Volume 198 (1988) no. 1, pp. 117-125 | DOI | MR | Zbl

[8] Helminck, A. G.; Wang, S. P. On rationality properties of involutions of reductive groups, Adv. Math., Volume 99 (1993) no. 1, pp. 26-96 | DOI | MR | Zbl

[9] Knop, Friedrich The Luna-Vust theory of spherical embeddings, Proceedings of the Hyderabad Conference on Algebraic Groups (Hyderabad, 1989) (1991), pp. 225-249 | MR | Zbl

[10] Kumar, Shrawan Proof of Wahl’s conjecture on surjectivity of the Gaussian map for flag varieties, Amer. J. Math., Volume 114 (1992) no. 6, pp. 1201-1220 | DOI | MR | Zbl

[11] Lakshmibai, V.; Mehta, V. B.; Parameswaran, A. J. Frobenius splittings and blow-ups, J. Algebra, Volume 208 (1998) no. 1, pp. 101-128 | DOI | MR | Zbl

[12] Lakshmibai, Venkatramani; Raghavan, Komaranapuram N.; Sankaran, Parameswaran Wahl’s conjecture holds in odd characteristics for symplectic and orthogonal Grassmannians, Cent. Eur. J. Math., Volume 7 (2009) no. 2, pp. 214-223 | DOI | MR | Zbl

[13] Lauritzen, Niels; Thomsen, Jesper Funch Maximal compatible splitting and diagonals of Kempf varieties, Ann. Inst. Fourier (Grenoble), Volume 61 (2011) no. 6, p. 2543-2575 (2012) | DOI | Numdam | MR | Zbl

[14] Littelmann, Peter On spherical double cones, J. Algebra, Volume 166 (1994) no. 1, pp. 142-157 | DOI | MR | Zbl

[15] Mehta, V. B.; Parameswaran, A. J. On Wahl’s conjecture for the Grassmannians in positive characteristic, Internat. J. Math., Volume 8 (1997) no. 4, pp. 495-498 | DOI | MR | Zbl

[16] Oda, Tadao Convex bodies and algebraic geometry, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), 15, Springer-Verlag, Berlin, 1988, pp. viii+212 | MR | Zbl

[17] Stembridge, John R. Multiplicity-free products and restrictions of Weyl characters, Represent. Theory, Volume 7 (2003), p. 404-439 (electronic) | DOI | MR | Zbl

[18] Thomsen, Jesper Funch A proof of Wahl’s conjecture in the symplectic case, Transform. Groups, Volume 18 (2013) no. 1, pp. 263-286 | DOI | MR | Zbl

[19] Vust, Thierry Opération de groupes réductifs dans un type de cônes presque homogènes, Bull. Soc. Math. France, Volume 102 (1974), pp. 317-333 | Numdam | MR | Zbl

[20] Wahl, Jonathan Gaussian maps and tensor products of irreducible representations, Manuscripta Math., Volume 73 (1991) no. 3, pp. 229-259 | DOI | MR | Zbl

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