关于Bezoutians的双线性结构
On the bilinear structure associated to Bezoutians
摘要：
本文是对二次型的已知结果的部分综述，这些结果在文献中很难找到。我们的主要焦点是由于Bezout的建筑扭曲的形式。这个斜Bezoutian是一个辛（resp.二次）空间，与一对同阶互素多项式相关。该空间的等距群原来包含某个相关的超几何群。使用斜Bezoutian我们构建明确的等距双线性空间与给定的不变量（如特征多项式或约旦形式，并在二次的情况下，旋量范）。
英文摘要：
This paper is partly a survey of known results on quadratic forms that are hard to find in the literature. Our main focus is a twisted form of a construction due to Bezout. This skew Bezoutian is a symplectic (resp. quadratic) space associated to a pair of reciprocal (or skew reciprocal) coprime polynomials of same degree. The isometry group of this space turns out to contain a certain associated hypergeometric group. Using the skew Bezoutian we construct explicit isometries of bilinear spaces with given invariants (such as the characteristic polynomial or Jordan form and, in the quadratic case, the spinor norm).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
