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Journal | Mathematical Proceedings of the Cambridge Philosophical Society |
---|---|

Date | Published - 1 May 2003 |

Issue number | 2 |

Volume | 134 |

Number of pages | 9 |

Pages (from-to) | 229-237 |

Original language | English |

In a recent paper [13], Kulkarni proves that, for i > 0, one has

Exti

G(M

();r())%Exti

G(M;r(=))

{ an isomorphism of spaces of extensions of rational modules. Here G is a general

linear group scheme, ; are partitions and M is a polynomial G-module. The modules

(), r() and r(=) are respectively the Weyl module labelled by , the

induced module labelled by and the skew module labelled by =. A similar result

is given in which the roles of and r are interchanged.

Our purpose here is to set this result in the context of the representation theory

of an arbitrary reductive group. Specically, we prove a simple result which is valid

for general reductive groups and derive Kulkarni's results from this. For convenience

we work over an algebraically closed eld k.

This paper is dedicated to Idun Reiten on the occasion of her 60th birthday.

Exti

G(M

();r())%Exti

G(M;r(=))

{ an isomorphism of spaces of extensions of rational modules. Here G is a general

linear group scheme, ; are partitions and M is a polynomial G-module. The modules

(), r() and r(=) are respectively the Weyl module labelled by , the

induced module labelled by and the skew module labelled by =. A similar result

is given in which the roles of and r are interchanged.

Our purpose here is to set this result in the context of the representation theory

of an arbitrary reductive group. Specically, we prove a simple result which is valid

for general reductive groups and derive Kulkarni's results from this. For convenience

we work over an algebraically closed eld k.

This paper is dedicated to Idun Reiten on the occasion of her 60th birthday.

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