Wahl’s conjecture holds in odd characteristics for symplectic and orthogonal Grassmannians

• Autorzy: Venkatramani Lakshmibai , Komaranapuram Raghavan , Parameswaran Sankaran
• Języki publikacji: EN

Abstrakty

EN

It is shown that the proof by Mehta and Parameswaran of Wahl’s conjecture for Grassmannians in positive odd characteristics also works for symplectic and orthogonal Grassmannians.

Słowa kluczowe

EN

Wahl’s conjecture; Frobenius splitting; Canonical splitting; Maximal multiplicity; Diagonal splitting; Grassmannians (ordinary, orthogonal, and symplectic)

Kategorie tematyczne

• 14M15: Grassmannians, Schubert varieties, flag manifolds
• 20G15: Linear algebraic groups over arbitrary fields

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2009
• Tom: 7
• Numer: 2
• Strony: 214-223

Daty

wydano

2009-06-01

online

2009-05-24

Twórcy

autor

Venkatramani Lakshmibai

• Northeastern University, Boston, USA

autor

Komaranapuram Raghavan

• Institute of Mathematical Sciences, C. I. T. Campus, Chennai, India

autor

Parameswaran Sankaran

• Institute of Mathematical Sciences, C. I. T. Campus, Chennai, India

Bibliografia

• [1] Bourbaki N., Éléments de mathématique. Fasc. XXXIV. Groupes et algèbres de Lie. Chapitre IV: Groupes de Coxeter et systèmes de Tits. Chapitre V: Groupes engendrés par des réflexions. Chapitre VI: systèmes de racines, Actualités Scientifiques et Industrielles, No. 1337, Hermann, Paris, 1968
• [2] Brion M., Kumar S., Frobenius splitting methods in geometry and representation theory, Progress in Mathematics, 231, Birkhäuser Boston, Inc., Boston, MA, 2005
• [3] Kumar S., Proof of Wahl’s conjecture on surjectivity of the Gaussian map for flag varieties, Amer. J. Math., 1992, 114, 1201–1220 http://dx.doi.org/10.2307/2374759[Crossref]
• [4] Lakshmibai V., Mehta V.B., Parameswaran A.J., Frobenius splittings and blow-ups, J. Algebra, 1998, 208, 101–128 http://dx.doi.org/10.1006/jabr.1998.7521[Crossref]
• [5] Mathieu O., Filtrations of G-modules, Ann. Sci. École Norm. Sup. (4), 1990, 23, 625–644
• [6] Mathieu O., Tilting modules and their applications, In: Analysis on homogeneous spaces and representation theory of Lie groups, Okayama-Kyoto (1997), Adv. Stud. Pure Math., 26, Math. Soc. Japan, Tokyo, 2000, 145–212
• [7] Mehta V.B., Parameswaran A.J., On Wahl’s conjecture for the Grassmannians in positive characteristic, Internat. J. Math., 1997, 8, 495–498 http://dx.doi.org/10.1142/S0129167X9700024X[Crossref]
• [8] Mehta V.B., Ramanathan A., Frobenius splitting and cohomology vanishing for Schubert varieties, Ann. of Math. (2), 1985, 122, 27–40 http://dx.doi.org/10.2307/1971368[Crossref]
• [9] Mehta V.B., Ramanathan A., Schubert varieties in G/B × G/B, Compositio Math., 1988, 67, 355–358
• [10] van der Kallen W., Lectures on Frobenius splittings and B-modules. Notes by S.P. Inamdar, Published for the Tata Institute of Fundamental Research, Bombay, by Springer-Verlag, Berlin, 1993
• [11] Wahl J., Gaussian maps and tensor products of irreducible representations, Manuscripta Math., 1991, 73, 229–259 http://dx.doi.org/10.1007/BF02567640[Crossref]

Identyfikatory

DOI

10.2478/s11533-009-0016-5