Positivity of Thom polynomials II: the Lagrange singularities

Abstract

We study Thom polynomials associated with Lagrange singularities. We expand them in the basis of Q-functions. This basis plays a key role in the Schubert calculus of isotropic Grassmannians. We prove that the Q-function expansions of Thom polynomials of Lagrange singularities have always nonnegative coefficients. This is an analog of a result on Thom polynomials of mapping singularities and Schur Sfunctions, established formerly by the two last authors.