Positivity of Thom polynomials II: the Lagrange singularities

Volume 202 / 2009

Małgorzata Mikosz, Piotr Pragacz, Andrzej Weber Fundamenta Mathematicae 202 (2009), 65-79 MSC: 05E05, 14C17, 14N15, 55R40, 57R45. DOI: 10.4064/fm202-1-3


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.


  • Małgorzata MikoszWarsaw University of Technology
    Pl. Politechniki 1
    00-661 Warszawa, Poland
  • Piotr PragaczInstitute of Mathematics
    Polish Academy of Sciences
    Śniadeckich 8
    00-956 Warszawa, Poland
  • Andrzej WeberDepartment of Mathematics
    Warsaw University
    Banacha 2
    02-097 Warszawa, Poland

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