TORUS ORBITS IN G/P

被引:29
作者
FLASCHKA, H [1 ]
HAINE, L [1 ]
机构
[1] UNIV ARIZONA,TUCSON,AZ 85721
关键词
D O I
10.2140/pjm.1991.149.251
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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 GIP by gP --> hgP. The closure X in GIP of an orbit {hgP/h member-of 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 torus-invariant 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 subset-of 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 .
引用
收藏
页码:251 / 292
页数:42
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