### Abstract

Let G be a complex semisimple Lie group of rank l, with fixed Borel subgroup B and maximal torus H. Let P be a standard parabolic subgroup. The torus H acts on G/P by gP → hgP. The closure X in G/P of an orbit {hgP\h ∈ H} is called a torus orbit if it is l-dimensional and satisfies a certain genericity condition; it is a rational algebraic variety whose structure is intimately related to Lie theory, symplectic geometry, and the theory of convex bodies. This paper presents: (1) an abstract description of the torus orbit X by means of a rational polyhedral fan; (2) a description of the torusinvariant divisor whose linear system provides a natural embedding (the Plucker embedding) of X into a projective space; (3) a discussion of the correspondence between this divisor and the momentum mapping associated to the action on X of the compact torus T ⊂ H (4) a list of generators of the ideal defining the Plucker embedding; (5) a formula for the intersection multiplicity of certain important torus invariant divisors on X.

Original language | English (US) |
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Pages (from-to) | 251-292 |

Number of pages | 42 |

Journal | Pacific Journal of Mathematics |

Volume | 149 |

Issue number | 2 |

State | Published - 1991 |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

*Pacific Journal of Mathematics*,

*149*(2), 251-292.