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

Magdalena Zielenkiewicz

Open Mathematics (2014)

  • Volume: 12, Issue: 4, page 574-583
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Magdalena Zielenkiewicz. "Integration over homogeneous spaces for classical Lie groups using iterated residues at infinity." Open Mathematics 12.4 (2014): 574-583. <http://eudml.org/doc/269799>.

@article{MagdalenaZielenkiewicz2014,
abstract = {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.},
author = {Magdalena Zielenkiewicz},
journal = {Open Mathematics},
keywords = {Grassmannian; Equivariant cohomology theory; Localization; Berline-Vergne formula; equivariant cohomology; integration; iterated residue},
language = {eng},
number = {4},
pages = {574-583},
title = {Integration over homogeneous spaces for classical Lie groups using iterated residues at infinity},
url = {http://eudml.org/doc/269799},
volume = {12},
year = {2014},
}

TY - JOUR
AU - Magdalena Zielenkiewicz
TI - Integration over homogeneous spaces for classical Lie groups using iterated residues at infinity
JO - Open Mathematics
PY - 2014
VL - 12
IS - 4
SP - 574
EP - 583
AB - 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.
LA - eng
KW - Grassmannian; Equivariant cohomology theory; Localization; Berline-Vergne formula; equivariant cohomology; integration; iterated residue
UR - http://eudml.org/doc/269799
ER -

References

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