Atlas of Lie Groups and Representations

Documentation contents

Script File

weyltosemisimple.at

Source
atlas-scripts/weyltosemisimple.at (90 lines)
Definitions
8
Loads
Loaded by
none of the other all.at files

Definitions in source order

shift_by_minus_1

L8shift_by_minus_1([int] S)
root numbering 0...n-1 versus 1...n
Commented-out code, lines 10–17 (6 lines)
set Kac_coordinates(RootDatum rd, ratvec v)=
let (v,d)=%v then
w=for alpha in simple_roots(rd) do alpha*v od then
affine=d-w*labels(rd) then
w_ratvec=w##[affine]/d in {do this to divide out common factor}
%w_ratvec

union

L19union([int] S,[int] T)

also defined in hodge_K_type_formula.at

good_data type

L21
set_type good_data = (RootDatum rd,string name,[([int],int)] pairs, int d,mat delta)

Fields: rd, name, pairs, d, delta

reverse_pairs

L23reverse_pairs(good_data data) = [([int],int)]

torus_element 2 overloads

L26torus_element(RootDatum rd,[int] S,int k) = ratvec
in X_*(T)_Q
L29torus_element(good_data data,bool shift_flag)

report

L58report([good_data] list) = void
V=X_*\otimes Q
V^\delta\subset V
V has a basis, making V\simeq Z^n
V^\delta has a basis, making V^\delta\simeq Z^m
P is an m\times n matrix, so that
P*[x_1,...,x_n]=[y_1,...,y_m]
where v=[x_1,...,x_n] in given basis of V
assume v\in V^\delta, then
v=[y_1,...,y_m] in given basis of V^delta
L66

coxeter_data

L77coxeter_data(RootDatum rd)
Commented-out code, lines 79–90 (9 lines)
{alternative output version}
set print(hodgeParamPol P)=void:
let header=["c","x","lambda","nu","codim_O","hwt","dim_K","height","mu"] then
values=for (c,p) in rearrange(P) do
let (,x)=%p.x then
(,,wt)=highest_weights(p)[0] in
[poly_format(c,"v"),x.to_string,p.lambda.to_string,p.nu.to_string,codim(x(p)).to_string,LKTs(p)[0].highest_weight.mu.to_string,LKTs(p)[0].dimension.to_string,
height(p).to_string,p.mu.to_string] od in
tabulate(header#values,"lllllllll",2," ")

Generated from atlas-scripts at commit 7e1b958 (2026-09-17).