### Abstract

Let G = SL_{n}(ℂ) ⋉ ℂ^{n} 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).

Original language | English (US) |
---|---|

Pages (from-to) | 1521-1532 |

Number of pages | 12 |

Journal | Science China Mathematics |

Volume | 54 |

Issue number | 8 |

DOIs | |

State | Published - Aug 2011 |

### Fingerprint

### Keywords

- affine groups
- linear group quotients
- rationality

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Science China Mathematics*,

*54*(8), 1521-1532. https://doi.org/10.1007/s11425-010-4127-z

**Rationality of quotients by linear actions of affine groups.** / Bogomolov, Fedor; Böhning, Christian; Graf von Bothmer, Hans Christian.

Research output: Contribution to journal › Article

*Science China Mathematics*, vol. 54, no. 8, pp. 1521-1532. https://doi.org/10.1007/s11425-010-4127-z

}

TY - JOUR

T1 - Rationality of quotients by linear actions of affine groups

AU - Bogomolov, Fedor

AU - Böhning, Christian

AU - Graf von Bothmer, Hans Christian

PY - 2011/8

Y1 - 2011/8

N2 - 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).

AB - 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).

KW - affine groups

KW - linear group quotients

KW - rationality

UR - http://www.scopus.com/inward/record.url?scp=80051685702&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80051685702&partnerID=8YFLogxK

U2 - 10.1007/s11425-010-4127-z

DO - 10.1007/s11425-010-4127-z

M3 - Article

AN - SCOPUS:80051685702

VL - 54

SP - 1521

EP - 1532

JO - Science China Mathematics

JF - Science China Mathematics

SN - 1674-7283

IS - 8

ER -