Differential forms on quotients

by reductive group actions

Author:
Michel Brion

Journal:
Proc. Amer. Math. Soc. **126** (1998), 2535-2539

MSC (1991):
Primary 14L30, 22E99

DOI:
https://doi.org/10.1090/S0002-9939-98-04320-2

MathSciNet review:
1451789

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a smooth affine algebraic variety where a reductive algebraic group acts with a smooth quotient space . We show that the algebraic differential forms on which are pull-backs of forms on are exactly the -invariant horizontal differential forms on .

**[B]**M. Brion:*Sur les modules de covariants*, Ann. scient. Éc. Norm. Sup.**26**(1993), p. 1-21. MR**95c:14062****[H]**R. Hartshorne:*Stable reflexive sheaves*, Math. Ann.**254**(1980), p. 121-176. MR**82b:14011****[K]**E. Kunz:*Kähler Differentials*, Viehweg, Braunschweig-Wiesbaden, 1986.MR**88e:14025****[L1]**D. Luna:*Slices étales*, Bull. Soc. math. France, Mémoire**33**(1973), p. 81-105. MR**49:7269****[L2]**D. Luna:*Adhérences d'orbites et invariants*, Invent. Math.**29**(1975), 231-238. MR**51:12879****[L-R]**D. Luna and R. W. Richardson:*A generalization of the Chevalley restriction theorem*, Duke Math. J.**46**(1979), p. 487-496. MR**80k:14049****[M1]**Peter W. Michor:*Basic differential forms for actions of Lie groups*, Proc. Amer. Math. Soc.**124**(1996), p. 1633-1642. MR**96g:57041****[M2]**Peter W. Michor:*Basic differential forms for actions of Lie groups II*, Proc. Amer. Math. Soc.**125**(1997), 2175-2177. CMP**97:10****[P-V]**V. L. Popov and E. B. Vinberg:*Invariant Theory*, Encyclopaedia of Mathematical Sciences, Algebraic Geometry IV, vol.**55**, Springer-Verlag, Berlin 1994, p. 123-284. MR**92d:14010****[So]**L. Solomon:*Invariants of finite reflection groups*, Nagoya Math. J.**22**(1963), p. 57-64. MR**27:4872**

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Additional Information

**Michel Brion**

Affiliation:
Institut Fourier, B. P. 74, 38402 Saint-Martin d’Hères Cedex, France

Email:
mbrion@fourier.ujf-grenoble.fr

DOI:
https://doi.org/10.1090/S0002-9939-98-04320-2

Received by editor(s):
October 25, 1996

Received by editor(s) in revised form:
January 29, 1997

Communicated by:
Roe Goodman

Article copyright:
© Copyright 1998
American Mathematical Society