【摘要】 设G是典型的代数群,B是它的Borel子群,W是与G相关的Weyl群。那末G可分解成不相交的B,B-双陪集BwB的并,其中w取遍Weyl群的所有元素。如果g是群G的元素,那末g该位于哪一个双陪集?对此本文提供了一个简便的判别方法,同时也得到了典型Weyl群每个元素的简约表示式。更多还原

【Abstract】 Let G be a classical algebraic group, B its Borel subgroup, W the Weyl grouprelative to G, then G is the disjoint union of the double cosets BwB, Where wruns over all elements of W. This paper provides a easy and simple criterion to determine which doublecosets g∈G lies in. Besides, We obtain a reduced expression for every element ofthe classical Weyl groups W.更多还原