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In mathematics, the Springer resolution is a resolution of the variety of nilpotent elements in a semisimple Lie algebra, or the unipotent elements of a reductive algebraic group, introduced by . The fibers of this resolution are called Springer fibers. If ''U'' is the variety of unipotent elements in a reductive group ''G'', and ''X'' the variety of Borel subgroups ''B'', then the Springer resolution of ''U'' is the variety of pairs (''u'',''B'') of ''U''×''X'' such that ''u'' is in the Borel subgroup ''B''. The map to ''U'' is the projection to the first factor. The Springer resolution for Lie algebras is similar, except that ''U'' is replaced by the nilpotent elements of the Lie algebra of ''G'' and ''X'' replaced by the variety of Borel subalgebras The Grothendieck–Springer resolution is defined similarly, except that ''U'' is replaced by the whole group ''G'' (or the whole Lie algebra of ''G''). When restricted to the unipotent elements of ''G'' it becomes the Springer resolution. ==References== * * * * * * * 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Springer resolution」の詳細全文を読む スポンサード リンク
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