[Next][Prev] [Right] [Left] [Up] [Index] [Root]

Related Structures

In this section we briefly list functions for creating other structures from a reflection group. See the appropriate chapters of the Handbook for more details.

CoxeterGroup(GrpFPCox, W) : Cat, GrpMat -> GrpPermCox
The Coxeter group isomorphic to the real reflection group W. See Chapter COXETER GROUPS.
CoxeterGroup(GrpPermCox, W) : Cat, GrpMat -> GrpPermCox
The permutation Coxeter group isomorphic to the finite real reflection group W. See Chapter COXETER GROUPS.
LieAlgebra(W, R) : GrpMat, Rng -> AlgLie
The reductive Lie algebraover the ring R with Weyl group W. Unless W is finite, real, and crystallographic, an error is flagged. See Section Almost Reductive Lie Algebras.
GroupOfLieType(W, k) : GrpMat, Rng -> GrpLie
The group of Lie typeover the field k with Weyl group W. Unless W is finite, real, and crystallographic, an error is flagged. The roots and coroots of W must also have integral components. See Chapter GROUPS OF LIE TYPE.
 [Next][Prev] [Right] [Left] [Up] [Index] [Root]

Version: V2.19 of Wed Apr 24 15:09:57 EST 2013