Decomposition Matrices
These functions interface with Thomas Breuer's package GenericDecMats
Chevie.InducedDecompositionMatrix
Chevie.Chars.decomposition_matrix
GenericDecMats.generic_decomposition_matrix
Chevie.Chars.decomposition_matrix
— Functiondecomposition_matrix(W,p)
This provides an interface to some decomposition matrices for Weyl groups available in the Chevie library: those for E₆, E₇, E₈
for p=2,3,5,7
.
GenericDecMats.generic_decomposition_matrix
— Functiongeneric_decomposition_matrix(W,d)
This function obtains the Φ_d
-decomposition matrix for the reductive group specified by the Coxeter group or coset W
from the package GenericDecMats.
julia> W=rootdatum(:psu,5)
psu₅
julia> generic_decomposition_matrix(W,13)
!!! Φ-decomposition matrices available for ²A₄: Φ₁₀ Φ₂ Φ₄ Φ₆
julia> generic_decomposition_matrix(W,10)
Φ₁₀-decomposition matrix for psu₅
│ps 21 ps ps ps 2111 11111
──────┼──────────────────────────
2. │ 1 . . . . . .
²A₂:2 │ . 1 . . . . .
11. │ . . 1 . . . .
1.1 │ 1 . . 1 . . .
.2 │ . . . . 1 . .
²A₂:11│ . 1 . . . 1 .
.11 │ . . . 1 . . 1
The matrix itself is stored in the field .scalar
of the returned struct
.
Chevie.InducedDecompositionMatrix
— TypeInducedDecompositionMatrix(R,W,d)
returns the induced from the Levi L
to the reductive group W
of the generic Φ_d
decomposition matrix of L
.
julia> W=rootdatum(:psu,6)
psu₆
julia> L=reflection_subgroup(W,[1,2,4,5])
psu₆₍₁₂₅₄₎=(A₂A₂)₍₁₂₄₃₎Φ₁
julia> InducedDecompositionMatrix(L,W,6)
Induced Φ₆-decomposition matrix from psu₆₍₁₂₅₄₎=(A₂A₂)₍₁₂₄₃₎Φ₁ to psu₆
│ps ps A₂
────┼─────────
²A₅ │ . . .
.3 │ 1 . .
3. │ 1 . .
.21 │ 1 1 .
1.2 │ 2 1 .
21. │ 1 1 .
2.1 │ 2 1 .
.111│ . 1 1
111.│ . 1 1
1.11│ 1 2 1
11.1│ 1 2 1
The matrix itself is stored in the field .scalar
of the returned struct
.