Geodesic
Positivity of Thom polynomials II: the Lagrange singularities
Małgorzata Mikosz 1   ; Piotr Pragacz 2   ; Andrzej Weber 3
1 Warsaw University of Technology Pl. Politechniki 1 00-661 Warszawa, Poland
2 Institute of Mathematics Polish Academy of Sciences Śniadeckich 8 00-956 Warszawa, Poland
3 Department of Mathematics Warsaw University Banacha 2 02-097 Warszawa, Poland
Fundamenta Mathematicae, Tome 202 (2009) no. 1, pp. 65-79 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/fm202-1-3
Keywords: study thom polynomials associated lagrange singularities expand basis tilde functions basis plays key role schubert calculus isotropic grassmannians prove tilde function expansions thom polynomials lagrange singularities always have nonnegative coefficients analog result thom polynomials mapping singularities schur s functions established formerly authors

Małgorzata Mikosz  1   ; Piotr Pragacz  2   ; Andrzej Weber  3

1 Warsaw University of Technology Pl. Politechniki 1 00-661 Warszawa, Poland
2 Institute of Mathematics Polish Academy of Sciences Śniadeckich 8 00-956 Warszawa, Poland
3 Department of Mathematics Warsaw University Banacha 2 02-097 Warszawa, Poland 
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Małgorzata Mikosz; Piotr Pragacz; Andrzej Weber. Positivity of Thom polynomials II:
 the Lagrange singularities. Fundamenta Mathematicae, Tome 202 (2009) no. 1, pp. 65-79. doi: 10.4064/fm202-1-3

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