Gap conditions for representations of symmetric groups
Gap conditions for representations of symmetric groups
复制标题
对称群表示的间隙条件
DOI：
10.1016/s0022-4049(96)00019-9
复制
发表时间：
1997
影响因子：
0.8
通讯作者：
M. Herzog
中科院分区：
文献类型：
--
作者：
K. Dovermann;M. Herzog
对于n ≥ 6的对称群S（n），我们构造表示，满足各种不动点集的维数的强间隙条件，如等变手术所需，以及各向同性群的条件，如构造具有有趣不动点集的流形所用。这使得我们可以构造S（n）在球面上的光滑作用，使得不动点集恰好是一个点，或者是任何给定的闭的、稳定可平行化的流形，其所有分量都具有相同的维数。
For the symmetric groups S(n) with n ≥ 6 we construct representations which satisfy a strong gap condition for the dimensions of various fixed point sets, as desired in equivariant surgery, and a condition on the isotropy groups, as used in the construction of manifolds with interesting fixed point sets. This allows us to construct smooth actions of S(n) on sphere such that the fixed point set is exactly one point, or any given closed, stably parallelizable manifold, all of whose components have the same dimension.