论文标题
多项式诱导和限制问题
Polynomial Induction and the Restriction Problem
论文作者
论文摘要
我们构建多项式诱导函数，这是限制函数的正确伴随，从一般线性组的多项式表示类别到其Weyl组的表示类别。这种构造导致了利特伍德的多个公式的表示形式证明，以在这种限制下对对称群体的多样性表示多样化。某些两部分分区函数的单峰性随之而来。
We construct the polynomial induction functor, which is the right adjoint to the restriction functor from the category of polynomial representations of a general linear group to the category of representations of its Weyl group. This construction leads to a representation-theoretic proof of Littlewood's plethystic formula for the multiplicity of an irreducible representation of the symmetric group in such a restriction. The unimodality of certain bipartite partition functions follows.
