报告题目：Projective Joint Spectra of operator tuples and representations of symmetry groups
报告人：Michael I. Stessin 教授 （纽约州立大学阿尔巴尼分校）
校内联系人：卢玉峰 教授 联系电话：84708351-8127
报告摘要: Projective Joint Spectra of operator tuples were introduced by R.Yang in 2008 and have been actively investigated since then. They generalize determinantal manifolds whose scrutiny started by Dickson in 1920s, and this area of interplay of operator theory and algebraic geometry is still very active today. Recent paper of Stessin and Tchernev concentrated on properties of operator tuples reflected in the geometry of the Projective Joint Spectrum. One of the results proved there implies that if pairwise joint spectra of a tuple of $n\times n$ unitary matrices consists of lines and "complex ellipses", then the group generated by these matrices represents a Coxeter group whose Coxeter matrix is determined by those ellipses. This leads to a natural question whether the joint spectrum of images of generators of a Coxeter group determines the representation up to equivalence. In the talk we will show that the answer is affirmative for symmetry groups $A_n, \ B_n$ and $I(n)$.