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 ChapGrpPermCox.

CoxeterGroup(GrpPermCox, W): Cat, GrpMat -> GrpPermCox

The permutation Coxeter group isomorphic to the finite real reflection group \(W\). See Chapter ChapGrpPermCox.

LieAlgebra(W, R): GrpMat, Rng -> AlgLie

The reductive Lie algebra over 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 type over 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.