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Schur and Schubert polynomials as Thom polynomials-cohomology of moduli spaces

László Fehér; Richárd Rimányi — 2003

Open Mathematics

The theory of Schur and Schubert polynomials is revisited in this paper from the point of view of generalized Thom polynomials. When we apply a general method to compute Thom polynomials for this case we obtain a new definition for (double versions of) Schur and Schubert polynomials: they will be solutions of interpolation problems.

The incidence class and the hierarchy of orbits

László Fehér; Zsolt Patakfalvi — 2009

Open Mathematics

R. Rimányi defined the incidence class of two singularities η and ζ as [η]|ζ, the restriction of the Thom polynomial of η to ζ. He conjectured that (under mild conditions) [η]|ζ ≠ 0 ⇔ ζ ⊂ $\bar{η}$ . Generalizing this notion we define the incidence class of two orbits η and ζ of a representation. We give a sufficient condition (positivity) for ζ to have the property that [η]|ζ ≠ 0 ⇔ ζ ⊂ $\bar{η}$ for any other orbit η. We show that for many interesting cases, e.g. the quiver representations of Dynkin type positivity...

On second order Thom-Boardman singularities

László M. Fehér; Balázs Kőműves — 2006

Fundamenta Mathematicae

We derive closed formulas for the Thom polynomials of two families of second order Thom-Boardman singularities $Σ^{i, j}$ . The formulas are given as linear combinations of Schur polynomials, and all coefficients are nonnegative.

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Currently displaying 1 – 3 of 3

Schur and Schubert polynomials as Thom polynomials-cohomology of moduli spaces

The incidence class and the hierarchy of orbits

On second order Thom-Boardman singularities