Integration over homogeneous spaces for classical Lie groups using iterated residues at infinity

• Autorzy: Magdalena Zielenkiewicz
• Języki publikacji: EN

Abstrakty

EN

Using the Berline-Vergne integration formula for equivariant cohomology for torus actions, we prove that integrals over Grassmannians (classical, Lagrangian or orthogonal ones) of characteristic classes of the tautological bundle can be expressed as iterated residues at infinity of some holomorphic functions of several variables. The results obtained for these cases can be expressed as special cases of one formula involving the Weyl group action on the characters of the natural representation of the torus.

Słowa kluczowe

EN

Grassmannian; Equivariant cohomology theory; Localization; Berline-Vergne formula

Kategorie tematyczne

• 14M15: Grassmannians, Schubert varieties, flag manifolds

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2014
• Tom: 12
• Numer: 4
• Strony: 574-583

Daty

wydano

2014-04-01

online

2014-01-17

Twórcy

autor

Magdalena Zielenkiewicz

• University of Warsaw

Bibliografia

• [1] Atiyah M.F., Bott R., The moment map and equivariant cohomology, Topology, 1984, 23(1), 1–28 http://dx.doi.org/10.1016/0040-9383(84)90021-1
• [2] Bérczi G., Szenes A., Thom polynomials of Morin singularities, Ann. of Math., 2012, 175(2), 567–629 http://dx.doi.org/10.4007/annals.2012.175.2.4
• [3] Berline N., Vergne M., Zéros d’un champ de vecteurs et classes caractéristiques équivariantes, Duke Math. J., 1983, 50(2), 539–549 http://dx.doi.org/10.1215/S0012-7094-83-05024-X
• [4] Borel A., Seminar on Transformation Groups, Ann. of Math. Stud., 46, Princeton University Press, Princeton, 1960
• [5] Fehér L.M., Rimányi R., Thom series of contact singularities, Ann. of Math., 2012, 176(3), 1381–1426 http://dx.doi.org/10.4007/annals.2012.176.3.1
• [6] Fulton W., Harris J., Representation Theory, Grad. Texts in Math., 129, Springer, New York, 1991 http://dx.doi.org/10.1007/978-1-4612-0979-9
• [7] Ginzburg V.A., Equivariant cohomology and Kähler geometry, Functional Anal. Appl., 1987, 21(4), 271–283 http://dx.doi.org/10.1007/BF01077801
• [8] Hsiang W., Cohomology Theory of Topological Transformation Groups, Ergeb. Math. Grenzgeb., 85, Springer, New York-Heidelberg, 1975 http://dx.doi.org/10.1007/978-3-642-66052-8
• [9] Jeffrey L.C., Kirwan F.C., Localization for nonabelian group actions, Topology, 1995, 34(2), 291–327 http://dx.doi.org/10.1016/0040-9383(94)00028-J
• [10] Jeffrey L.C., Kirwan F.C., Intersection theory on moduli spaces of holomorphic bundles of arbitrary rank on a Riemann surface, Ann. of Math., 1998, 148(1), 109–196 http://dx.doi.org/10.2307/120993
• [11] Kazarian M., On Lagrange and symmetric degeneracy loci, preprint available at http://www.newton.ac.uk/preprints/NI00028.pdf
• [12] Quillen D., The spectrum of an equivariant cohomology ring: I, Ann. of Math., 1971, 94(3), 549–572 http://dx.doi.org/10.2307/1970770
• [13] Rimányi R., Quiver polynomials in iterated residue form, preprint available at http://arxiv.org/abs/1302.2580
• [14] Weber A., Equivariant Chern classes and localization theorem, J. Singul., 2012, 5, 153–176

Identyfikatory

DOI

10.2478/s11533-013-0372-z