#### DMCA

## JEFFREY-KIRWAN-WITTEN LOCALIZATION FORMULA FOR REDUCTIONS AT REGULAR CO-ADJOINT ORBITS (1998)

### Citations

89 |
Localization for nonabelian group actions. Topology 34
- Jeffrey, Kirwan
- 1995
(Show Context)
Citation Context ...fibration µ −1 (O) → M O red . Remark 1.5. The localization formula and, in particular, this conjecture were proved for G = S 1 by Kalkman [4] and Wu [7], for general G and O = {0} by Jeffrey, Kirwan =-=[3]-=- and then modified by M. Vergne [6]. We prove this formula by using the universal orbital formula for characters by Kirillov [5]. 2. Proof of Theorem 1.1 2.1. Local Fourier Transform. Let us recall th... |

60 |
Elements of the Theory of Representations, Springer-Verlag
- Kirillov
- 1976
(Show Context)
Citation Context ...by Kalkman [4] and Wu [7], for general G and O = {0} by Jeffrey, Kirwan [3] and then modified by M. Vergne [6]. We prove this formula by using the universal orbital formula for characters by Kirillov =-=[5]-=-. 2. Proof of Theorem 1.1 2.1. Local Fourier Transform. Let us recall the main moments in Vergne’s modification for Jeffrey-Kirwan-Witten localization theorem. Recall that the group G acts on M by a H... |

57 |
Michèle Vergne, Heat kernels and Dirac operators, Grundlehren Text
- Berline, Getzler
- 2004
(Show Context)
Citation Context ...hat M is oriented and α ∈ A∞ G (g, M) such that ∀X ∈ g, supp α(X) is contained in a compact. One defines then ∫ ∫ α(X) = α(X)[n]. if n = dim M and α(X) is decomposed into a sum M α(X) = α(X)[0] + α(X)=-=[1]-=- + · · · + α(X)[n] of homogeneous differential forms α(X)[i] of degree i. MThis means that one has a map ∫ : AG(g, M) → C ∞ (g) G . M Suppose that our manifold M is closed, ∂M = ∅. Then because ı(XM)... |

32 |
Cohomology rings of symplectic quotients
- Kalkman
(Show Context)
Citation Context ... is the Chern-Weil homomorphism, associated to the principal fibration µ −1 (O) → M O red . Remark 1.5. The localization formula and, in particular, this conjecture were proved for G = S 1 by Kalkman =-=[4]-=- and Wu [7], for general G and O = {0} by Jeffrey, Kirwan [3] and then modified by M. Vergne [6]. We prove this formula by using the universal orbital formula for characters by Kirillov [5]. 2. Proof ... |

23 | An integration formula for the square of moment maps of circle actions, preprint hep-th/9212071 - Wu |

10 | A note on Jeffrey-Kirwan-Witten’s localisation formula, Topology 35
- Vergne
- 1996
(Show Context)
Citation Context ...rk 1.5. The localization formula and, in particular, this conjecture were proved for G = S 1 by Kalkman [4] and Wu [7], for general G and O = {0} by Jeffrey, Kirwan [3] and then modified by M. Vergne =-=[6]-=-. We prove this formula by using the universal orbital formula for characters by Kirillov [5]. 2. Proof of Theorem 1.1 2.1. Local Fourier Transform. Let us recall the main moments in Vergne’s modifica... |