Centraliser le marginal

The Index of a Lie Algebra, the Centraliser of a Nilpotent Element, and the Normaliser of the Centraliser

This definition goes back to J.Dixmier, see [Di, 11.1.6]. He considered index because of its importance in Representation Theory. The problem of computing the index may also be treated as part of Invariant Theory. For, if q is an algebraic Lie algebra and Q is a corresponding algebraic group, then ind q equals the transcendence degree of the field of Q-invariant rational functions on q. If q is...

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The symplectic ideal and a double centraliser theorem

We interpret a result of Oehms as a statement about the symplectic ideal. We use this result to prove a double centraliser theorem for the symplectic group acting on ⊕s r=0 ⊗ V , where V is the natural module for the symplectic group. This result was obtained in characteristic zero by Weyl. Furthermore, we use this to extend to arbitrary connected reductive groups G with simply connected derive...

Le livre est tout le problème

The search into new ways of writing is confronted with certain obstacles, the foremost of which is that of the book and its conventions inherited from 536 years of existence. Yet, literature is by in large independent of the particular medium that is the book, as reminds us the age-old oral tradition or the contemporary research of the Oulipo. The incursion of the computer into literature has t...

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