Atlas of Lie Groups and Representations

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atlas Library · Script File

cross_W_orbit.at

Source
atlas-scripts/cross_W_orbit.at (40 lines)
Definitions
4
Loads
Loaded by
W_K.at representations.at

Definitions in source order

cross_sub_orbit

L5cross_sub_orbit ([WeylElt] gens, KGBElt x) = [KGBElt,WeylElt]
orbit of |x| by cross actions from |gens|, with example transporting |w|

cross_orbit

L16cross_orbit (KGBElt x) = [KGBElt,WeylElt]

is_in_cross_orbit

L20is_in_cross_orbit (KGBElt x) = (KGBElt->bool,WeylElt)
whether |y| is in cross orbit of |x|, and if so a witness

cross_divide

L30cross_divide (KGBElt y,KGBElt x) = WeylElt
solve for w in W in y=cross(w,x); at least one solution should exist
note argument order

Generated from atlas-scripts at commit 648506c (2026-10-13).