Filip Jonsson Kling: On maximal rank properties for symmetric polynomials

Abstract: It is well known that a monomial complete intersection has the strong Lefschetz property in characteristic zero. This property is equivalent to the statement that any power of the sum of the variables is a maximal rank element on the complete intersection. In this talk, we will investigate what happens when this element is replaced by another symmetric polynomial, in an equigenerated complete intersection. We will first give the main ideas for how to answer the question completely for the power sum symmetric polynomial using a grading technique, and later for any Schur polynomial in the case of two variables by deriving a closed formula for the determinants of a family of Toeplitz matrices. In the end, several open questions will be mentioned.