Equivariant degenerations of spherical modules for groups of type A
Equivariant degenerations of spherical modules for groups of type A
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A 型群的球形模的等变退化
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
B. V. Steirteghem
中科院分区：
文献类型：
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作者：
Stavros A. Papadakis;B. V. Steirteghem
设G是复约化代数群.设G的一个Borel子群B，其根U是幂幺的，且极大环面T在B中，其特征标群为X（T）.设S是X（T）的一个由n个支配权生成的子幺半群. V. Alexeev和M. Brion引入了一个模概型M_S，它对（X，f）进行分类，其中X是仿射G-簇，f是X与U的范畴商与S所确定的环面簇之间的T-等变同构。本文证明了当S是具有A型G的球面G-模的权幺半群时，M_S同构于仿射空间。
Let G be a complex reductive algebraic group. Fix a Borel subgroup B of G, with unipotent radical U, and a maximal torus T in B with character group X(T). Let S be a submonoid of X(T) generated by finitely many dominant weights. V. Alexeev and M. Brion introduced a moduli scheme M_S which classifies pairs (X,f) where X is an affine G-variety and f is a T-equivariant isomorphism between the categorical quotient of X by U and the toric variety determined by S. In this paper, we prove that M_S is isomorphic to an affine space when S is the weight monoid of a spherical G-module with G of type A.