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

Venkatramani Lakshmibai; Komaranapuram Raghavan; Parameswaran Sankaran

Open Mathematics (2009)

  • Volume: 7, Issue: 2, page 214-223
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Venkatramani Lakshmibai, Komaranapuram Raghavan, and Parameswaran Sankaran. "Wahl’s conjecture holds in odd characteristics for symplectic and orthogonal Grassmannians." Open Mathematics 7.2 (2009): 214-223. <http://eudml.org/doc/269207>.

@article{VenkatramaniLakshmibai2009,
abstract = {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.},
author = {Venkatramani Lakshmibai, Komaranapuram Raghavan, Parameswaran Sankaran},
journal = {Open Mathematics},
keywords = {Wahl’s conjecture; Frobenius splitting; Canonical splitting; Maximal multiplicity; Diagonal splitting; Grassmannians (ordinary, orthogonal, and symplectic); Wahl's conjecture; canonical splitting; maximal multiplicity; diagonal splitting; Grassmannians},
language = {eng},
number = {2},
pages = {214-223},
title = {Wahl’s conjecture holds in odd characteristics for symplectic and orthogonal Grassmannians},
url = {http://eudml.org/doc/269207},
volume = {7},
year = {2009},
}

TY - JOUR
AU - Venkatramani Lakshmibai
AU - Komaranapuram Raghavan
AU - Parameswaran Sankaran
TI - Wahl’s conjecture holds in odd characteristics for symplectic and orthogonal Grassmannians
JO - Open Mathematics
PY - 2009
VL - 7
IS - 2
SP - 214
EP - 223
AB - 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.
LA - eng
KW - Wahl’s conjecture; Frobenius splitting; Canonical splitting; Maximal multiplicity; Diagonal splitting; Grassmannians (ordinary, orthogonal, and symplectic); Wahl's conjecture; canonical splitting; maximal multiplicity; diagonal splitting; Grassmannians
UR - http://eudml.org/doc/269207
ER -

References

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  1. [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 Zbl0186.33001
  2. [2] Brion M., Kumar S., Frobenius splitting methods in geometry and representation theory, Progress in Mathematics, 231, Birkhäuser Boston, Inc., Boston, MA, 2005 Zbl1072.14066
  3. [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] Zbl0790.14015
  4. [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] Zbl0955.14006
  5. [5] Mathieu O., Filtrations of G-modules, Ann. Sci. École Norm. Sup. (4), 1990, 23, 625–644 Zbl0748.20026
  6. [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. [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] Zbl0914.14021
  8. [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] Zbl0601.14043
  9. [9] Mehta V.B., Ramanathan A., Schubert varieties in G/B × G/B, Compositio Math., 1988, 67, 355–358 
  10. [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. [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] Zbl0764.20022

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