A system of quadrics describing the orbit of the highest weight vector
HTML articles powered by AMS MathViewer
- by Woody Lichtenstein PDF
- Proc. Amer. Math. Soc. 84 (1982), 605-608 Request permission
Abstract:
Let $G$ be a complex semisimple Lie group acting irreducibly on a finite dimensional vector space $V$. A simple method is given for constructing a system of quadratic equations which defines the orbit of the highest weight vector in the projective space $PV$.References
- Daniel Drucker, Exceptional Lie algebras and the structure of Hermitian symmetric spaces, Mem. Amer. Math. Soc. 16 (1978), no. 208, iv+207. MR 499340, DOI 10.1090/memo/0208
- Hans Freudenthal, Sur le groupe exceptionnel $E_7$, Nederl. Akad. Wetensch. Proc. Ser. A. 56=Indagationes Math. 15 (1953), 81–89 (French). MR 0054609
- Phillip Griffiths and Joseph Harris, Principles of algebraic geometry, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York, 1978. MR 507725
- Nathan Jacobson, Structure and representations of Jordan algebras, American Mathematical Society Colloquium Publications, Vol. XXXIX, American Mathematical Society, Providence, R.I., 1968. MR 0251099
- André Lichnerowicz, Sur les espaces homogènes kählériens, C. R. Acad. Sci. Paris 237 (1953), 695–697 (French). MR 66016
- Roger Marlin, Anneaux de Chow des groupes algébriques $\textrm {SU}(n)$, $\textrm {Sp}(n)$, $\textrm {SO}(n)$, $\textrm {Spin}(n)$, $G_{2}$, $F_{4}$; torsion, C. R. Acad. Sci. Paris Sér. A 279 (1974), 119–122 (French). MR 347820
- Deane Montgomery, Simply connected homogeneous spaces, Proc. Amer. Math. Soc. 1 (1950), 467–469. MR 37311, DOI 10.1090/S0002-9939-1950-0037311-6 J. P. Serre, Représentations linéaires et espaces homogènes Kählériens des groupes de Lie compacts, Séminaire Bourbaki No. 100, 1954.
- J. Tits, Le plan projectif des octaves et les groupes exceptionnels $E_6$ et $E_7$, Acad. Roy. Belgique. Bull. Cl. Sci. (5) 40 (1954), 29–40 (French). MR 0062749 —, Sur certaines classes d’espaces homogènes de groupes de Lie, Acad. Roy. Belg. Cl. Sci. Mem. Collect. 29 (1955-56).
- Hsien-Chung Wang, Closed manifolds with homogeneous complex structure, Amer. J. Math. 76 (1954), 1–32. MR 66011, DOI 10.2307/2372397
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 84 (1982), 605-608
- MSC: Primary 14M15; Secondary 15A75, 20G05
- DOI: https://doi.org/10.1090/S0002-9939-1982-0643758-8
- MathSciNet review: 643758