Statements (24)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Weyl_group
|
| gptkbp:actsOn |
root system of type A_n
|
| gptkbp:actsSimplyTransitivelyOn |
chambers of the Coxeter complex of type A_n
|
| gptkbp:appearsIn |
gptkb:Lie_theory
gptkb:algebraic_geometry representation theory combinatorics |
| gptkbp:associatedWith |
Lie algebra of type A_n
|
| gptkbp:CoxeterPresentation |
(S, R) with S = {s_1, ..., s_n}, R = {s_i^2 = 1, (s_i s_{i+1})^3 = 1, (s_i s_j)^2 = 1 for |i-j|>1}
|
| gptkbp:Dynkin_diagram |
A_n (linear diagram with n nodes)
|
| gptkbp:generation |
simple transpositions (i, i+1)
|
| https://www.w3.org/2000/01/rdf-schema#label |
Weyl group of type A n
|
| gptkbp:isFinite |
true
|
| gptkbp:isomorphicTo |
gptkb:symmetric_group_S_{n+1}
|
| gptkbp:notation |
S_{n+1}
W(A_n) |
| gptkbp:order |
(n+1)!
|
| gptkbp:reflectionGroup |
true
|
| gptkbp:relatedTo |
gptkb:Weyl_group
gptkb:root permutation group Dynkin diagram of type A_n |
| gptkbp:bfsParent |
gptkb:A_n_root_lattice
|
| gptkbp:bfsLayer |
6
|