- Introduction
- Construction of Pseudo- reflections
- PseudoReflection(a, b) : ModTupRngElt, ModTupRngElt -> AlgMatElt
- Transvection(a, b) : ModTupRngElt, ModTupRngElt -> AlgMatElt
- Reflection(a, b) : ModTupRngElt, ModTupRngElt -> AlgMatElt
- IsPseudoReflection(r) : Mtrx -> BoolElt, ModTupRngElt, ModTupRngElt
- IsTransvection(r) : Mtrx -> BoolElt, ModTupRngElt, ModTupRngElt
- IsReflection(r) : Mtrx -> BoolElt, ModTupRngElt, ModTupRngElt
- IsReflectionGroup(G) : GrpMat -> BoolElt
- Example GrpRfl_pseudoreflection (H106E1)
- Example GrpRfl_ref-group (H106E2)
- Example GrpRfl_transvections (H106E3)
- Pseudo-reflections Preserving Reflexive Forms
- Construction of Reflection Groups
- Construction of Real Reflection Groups
- Construction of Finite Complex Reflection Groups
- ShephardTodd(n) : RngIntElt -> GrpMat, Fld
- Example GrpRfl_ComplexReflectionGroups (H106E9)
- ComplexReflectionGroup(C) : Mtrx -> GrpMat, Map
- ComplexReflectionGroup(X, n) : MonStgElt, RngIntElt -> GrpMat, Map
- Example GrpRfl_reflection-subgroups (H106E10)
- ShephardTodd(m, p, n) : RngIntElt, RngIntElt, RngIntElt -> GrpMat, Fld
- Example GrpRfl_ImprimitiveReflectionGroup (H106E11)
- ComplexRootMatrices(k) : RngIntElt -> AlgMatElt, AlgMatElt, AlgMatElt, RngElt, RngIntElt
- Example GrpRfl_ComplexReflectionGroupByMatrix (H106E12)
- ComplexCartanMatrix(k) : RngIntElt -> AlgMatElt
- BasicRootMatrices(C) : Mtrx -> AlgMatElt, AlgMatElt
- CohenCoxeterName(k) : RngIntElt -> MonStgElt, RngIntElt
- ShephardToddNumber(X, n) : MonStgElt, RngIntElt -> RngIntElt
- Example GrpRfl_NameConversion (H106E13)
- Example GrpRfl_ReflectionGroupNames (H106E14)
- ComplexRootDatum(k) : RngIntElt -> SeqEnum, SeqEnum, Map, GrpMat, AlgMatElt
- Operations on Reflection Groups
- IsCoxeterIsomorphic(W1, W2) : GrpMat, GrpMat -> BoolElt
- IsCartanEquivalent(W1, W2) : GrpMat, GrpMat -> BoolElt
- Example GrpRfl_Isomorphism (H106E15)
- CartanName(W) : GrpMat -> List
- CoxeterDiagram(W) : GrpMat ->
- DynkinDiagram(W) : GrpMat ->
- Example GrpRfl_NameAndDiagram (H106E16)
- RootSystem(W) : GrpMat -> RootDtm
- RootDatum(W) : GrpMat -> RootDtm
- CoxeterMatrix(W) : GrpMat -> AlgMatElt
- CoxeterGraph(W) : GrpMat -> GrphUnd
- CartanMatrix(W) : GrpMat -> AlgMatElt
- DynkinDigraph(W) : GrpMat -> GrphDir
- Rank(W) : GrpMat -> RngIntElt
- Example GrpRfl_RankDimension (H106E17)
- FundamentalGroup(W) : GrpMat -> GrpAb
- IsogenyGroup(W) : GrpMat -> GrpAb, Map
- CoisogenyGroup(W) : GrpMat -> GrpAb, Map
- BasicDegrees(W) : GrpMat -> RngIntElt
- BasicCodegrees(W) : GrpMat -> RngIntElt
- Example GrpRfl_BasicDegrees (H106E18)
- LongestElement(W) : GrpMat -> SeqEnum
- CoxeterElement(W) : GrpMat -> SeqEnum
- CoxeterNumber(W) : GrpMat -> SeqEnum
- Example GrpRfl_Operations (H106E19)
- LeftDescentSet(W, w) : GrpMat, GrpMatElt ->()
- RightDescentSet(W, w) : GrpMat, GrpMatElt ->()
- Example GrpRfl_DescentSets (H106E20)
- Properties of Reflection Groups
- Roots, Coroots and Reflections
- Related Structures
- Bibliography
V2.28, 13 July 2023