@article{b011dcf3655c4fa89f9b8801ec94a2de,

title = "Rationality of quotients by linear actions of affine groups",

abstract = "Let G = SLn(ℂ) ⋉ ℂn be the (special) affine group. In this paper we study the representation theory of G and in particular the question of rationality for V/G, where V is a generically free G-representation. We show that the answer to this question is positive (Theorem 6.1) if the dimension of V is sufficiently large and V is indecomposable. We explicitly characterize two-step extensions 0 → S → V → Q → 0, with completely reducible S and Q, whose rationality cannot be obtained by the methods presented here (Theorem 5.3).",

keywords = "affine groups, linear group quotients, rationality",

author = "Fedor Bogomolov and Christian B{\"o}hning and {Graf von Bothmer}, {Hans Christian}",

note = "Funding Information: Acknowledgements During the work, the first author was supported by the Natural Science Foundation of USA (Grant No. DMS 0701578). He also wants to thank Korean Institute of Advanced Study and Institut des Hautes {\'E}tudes Scientifiques for hospitality and support during the work on the paper. The second and third authors were supported by the German Research Foundation (Deutsche Forschungsgemeinschaft (DFG)) through the Institutional Strategy of the University of G{\"o}ttingen. The second author thanks IH{\'E}S for hospitality during a stay when this work was started.",

year = "2011",

month = aug,

doi = "10.1007/s11425-010-4127-z",

language = "English (US)",

volume = "54",

pages = "1521--1532",

journal = "Science China Mathematics",

issn = "1674-7283",

publisher = "Science in China Press",

number = "8",

}