Duale Varietäten von Fahnenvarietäten

Knop F, Menzel G (1987)

Publication Language: German

Publication Status: Published

Publication Type: Journal article, Original article

Publication year: 1987

Journal

Commentarii Mathematici Helvetici European Mathematical Society / Springer Verlag (Germany)

Publisher: European Mathematical Society / Springer Verlag (Germany)

Book Volume: 62

Pages Range: 38-61

Journal Issue: 1

DOI: 10.5169/seals-47339

Abstract

Let V be an irreducible representation of a semisimple algebraic group G and X the orbit of an highest weight vector in the projective spave P(V). Then X is a generalized flag variety. The dual variety of X is the set of hyperplanes in P(V) which are tangent to X.

The purpose of the paper is to determine all cases in which the dual variety is not of codimension one. When G is simple there are the following cases (upto isomorphims of G and V):

G=SL(n,k), V=kⁿ; G=Sp_n, V=kⁿ (n even); G=SL(n,k), V=\wedge²kⁿ (n odd); G=Spin(9) or Spin(10), V=k¹⁶.

The classification for semisimple groups is easily obtained from that.

Authors with CRIS profile

Friedrich Knop Lehrstuhl für Mathematik (Algebra und Geometrie)

How to cite

APA:

Knop, F., & Menzel, G. (1987). Duale Varietäten von Fahnenvarietäten. Commentarii Mathematici Helvetici, 62(1), 38-61. https://doi.org/10.5169/seals-47339

MLA:

Knop, Friedrich, und Gisela Menzel. "Duale Varietäten von Fahnenvarietäten." Commentarii Mathematici Helvetici 62.1 (1987): 38-61.

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