Root datum: Difference between revisions

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Revision as of 02:02, 24 February 2007

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==Definition==

A '''root datum''' consists of a quadruple <math>(''X'', \&Psi;, ''X^{\vee}^&or;, \&Psi^{\vee}) <sup>&or;</mathsup>), where :

*<math>X, X^{\vee}</math> are free abelian groups of finite [[rank]] together with a perfect pairing <math>\langle , \rangle : X \times X^{\vee} \rightarrow \mathbf{Z}</math> between them (in other words, each is identified with the [[dual lattice]] of the other).