Advanced search
Publication Cover
Experimental Mathematics Volume 15, 2006 - Issue 4
Submit an article Journal homepage
19
Views
0
CrossRef citations to date
0
Altmetric
Original Article

Prehomogeneous Spaces Associated with Nilpotent Orbits in Simple Real Lie Algebras E6(6) and E6(-26) and Their Relative Invariants

Steven Glenn Jackson Department of Mathematics, University of Massachusetts, 100 Morrissey Boulevard, Boston, MA 02125-3393
&
Alfred G. Noël Department of Mathematics, University of Massachusetts, 100 Morrissey Boulevard, Boston, MA 02125-3393
Pages 455-469 | Published online: 30 Jan 2011

  • Dragomir Ž. Ðoković. "Classification of Nilpotent Elements in Simple Exceptional Real Lie Algebras of Inner Type and Description of Their Centralizers." J. Algebra 112:2 (1988), 503–524.
  • Dragomir Ž. Ðoković. "Classification of Nilpotent Elements in Simple Real Lie Algebras E 6(6) and E 6(-26) and Description of Their Centralizers." J. Algebra 116:1 (1988), 196–207.
  • Steven Glenn Jackson and Alfred G. Noël. "Prehomogeneous Spaces Associated with Complex Nilpotent Orbits." J. Algebra 289:2 (2005), 515–557.
  • "A LiE Subroutine for Computing Prehomogeneous Spaces Associated with Complex Nilpotent Orbits." In ICCS 2005, Lecture Notes in Computer Science, 3516, pp. 611–618. Berlin: Springer, 2005.
  • "A LiE Subroutine for Computing Prehomogeneous Spaces Associated with Real Nilpotent Orbits." In ICCSA 2005, Lecture Notes in Computer Science, 3482, pp. 512–521. Berlin: Springer, 2005.
  • "Prehomogeneous Spaces Associated with Real Nilpotent Orbits." J. Algebra 305:1 (2006), 194–269.
  • V. G. Kac. "Some Remarks on Nilpotent Orbits." J. Algebra 64:1 (1980), 190–213.
  • Anthony W. Knapp. Lie Groups: Beyond an Introduction, Progress in Mathematics, 140. Boston: Birkhäuser, 2002.
  • B. Kostant and S. Rallis. "Orbits and Representations Associated with Symmetric Spaces." Amer. J. Math. 93 (1971), 753–809.
  • Alfred G. Noël. "Nilpotent Orbits and Theta-Stable Parabolic Subalgebras." Represent. Theory 2 (1998), Article 99g:17023, 1–32.
  • Takuya Ohta. "Classification of Admissible Nilpotent Orbits in the Classical Real Lie Algebras." J. Algebra 136:2 (1991), 290–333.
  • Hubert Rubenthaler. Algèbres de Lie et espaces préhomogènes, Travaux en cours, 44. Paris: Hermann, 1992.
  • M. Sato and T. Kimura. "A Classification of Irreducible Prehomogeneous Vector Spaces and Their Relative Invariants." 65 (1977), 1–155.
  • Jirō Sekiguchi. "Remarks on Real Nilpotent Orbits of a Symmetric Pair." J. Math. Soc. Japan 39:1 (1987), 127–138.
  • T. A. Springer and R. Steinberg. "Conjugacy Classes." In Seminar on Algebraic Groups and Related Finite Groups (The Institute for Advanced Study, Princeton, N.J., 1968/69), Lecture Notes in Mathematics 131, pp. 167–266. Berlin: Springer, 1970.
  • Michèle Vergne. "Instantons et correspondance de Kostant–Sekiguchi." C. R. Acad. Sci. Paris Sér. I Math. 320:8 (1995), 901–906.
  • È. B. Vinberg. "The Classification of Nilpotent Elements of Graded Lie Algebras." Soviet Math. Dokl. 16:6 (1975), 1517–1520.
  • È. B. Vinberg. "The Weyl Group of a Graded Lie Algebra." Math. USSR-Izv. 10 (1976), 463–495.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.