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The incidence class and the hierarchy of orbits

100%

Fehér L., Patakfalvi Z.

Open Mathematics

2009

tom 7

nr 3

429-441

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 ⊂ $$ \bar \eta $$. 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 ⊂ $$ \bar \eta $$ for any other orbit η. We show that for many interesting cases, e.g. the quiver representations of Dynkin type positivity holds for all orbits. In other words in these cases the incidence classes completely determine the hierarchy of the orbits. We also study the case of singularities where positivity doesn’t hold for all orbits.

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

100%

Fehér L., Rimányi R.

Open Mathematics

2003

tom 1

nr 4

418-434

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.

Ograniczanie wyników

2 Open Mathematics

2 Fehér L.

1 Patakfalvi Z.

1 Rimányi R.

1 2009

1 2003

Wyniki wyszukiwania

The incidence class and the hierarchy of orbits

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