Positivity of Thom polynomials II: the Lagrange singularities
Volume 202 / 2009
Fundamenta Mathematicae 202 (2009), 65-79
MSC: 05E05, 14C17, 14N15, 55R40, 57R45.
DOI: 10.4064/fm202-1-3
Abstract
We study Thom polynomials associated with Lagrange singularities. We expand them in the basis of ${\tilde Q}$-functions. This basis plays a key role in the Schubert calculus of isotropic Grassmannians. We prove that the ${\tilde Q}$-function expansions of the Thom polynomials of Lagrange singularities always have nonnegative coefficients. This is an analog of a result on the Thom polynomials of mapping singularities and Schur $S$-functions, established formerly by the last two authors.
