1 | initial version |
I answer myself, just in case someone finds this and have the same problem:
My bad: the solution to the "strange" fundamental weights is explained in http://www.sagemath.org/doc/thematic_tutorials/lie/weyl_character_ring.html#sl-versus-gl.
Following the example:
sage: [fw.coerce_to_sl() for fw in A2.fundamental_weights()]
[(2/3, -1/3, -1/3), (1/3, 1/3, -2/3)]
Anyway, I am considering proposing to add a style='coroots' option to weight_multiplicities() to get the output in 'Dynkin labels'.
Cheers!