We use cookies to ensure that we give you the best experience on our website. You can change your cookie settings at any time. Otherwise, we'll assume you're OK to continue.

Department of Mathematical Sciences

Seminar Archives

"The Wronski map associates to a $p$-tuple of polynomials of degree $m+p-1$ their Wronski determinant, a polynomial of degree $mp$. If the polynomials are linearly independent, they define a a point in the Grassmannian $G(p,m+p)$. Accordingly, the Wronski map can be considered as a map from $G(p,m+p)$ to the projective space ${\bf P}^{mp}$. The map is finite, and one can define its degree. In the complex case, this degree equals the number of standard Young tableaux for the rectangular $(m,p)$-shape. In the real case, Young tableax should be counted with the signs depending on the number of inversions. Degree of the real Wronski map is zero when $m+p$ is even, and equals the number of standard shifted Young tableaux for an appropriately defined shifted shape when $m+p$ is odd. When both $m$ and $p$ are even, the Wronski map is not surjective. These results have important applications to real Schubert Calculus and to the pole placement problem in control theory. "