# Revision history [back]

You can get the coroot vector from the inner product with the simple coroots, of course:

sage: B5 = WeylCharacterRing('B5',style='coroots')
sage: Rep = 2*B5(1,0,0,0,0) + B5(0,1,2,3,0)
sage: Rep.degree()    # dimension
3777283147
sage: for highest_weight, multiplicity in Rep:
....:     coroots = [ highest_weight.inner_product(coroot)
....:                 for coroot in list(B5.simple_coroots()) ]
....:     print coroots, highest_weight, multiplicity
....:
[1, 0, 0, 0, 0] (1, 0, 0, 0, 0) 2
[0, 1, 2, 3, 4] (8, 8, 7, 5, 2) 1


Note that I used a more complicated group where simple roots do not coincide with the simple coroot vectors as in SU(4).

You can get the coroot vector components from the inner product with the simple coroots, of course:

sage: B5 = WeylCharacterRing('B5',style='coroots')
sage: Rep = 2*B5(1,0,0,0,0) + B5(0,1,2,3,0)
sage: Rep.degree()    # dimension
3777283147
sage: for highest_weight, multiplicity in Rep:
....:     coroots = [ highest_weight.inner_product(coroot)
....:                 for coroot in list(B5.simple_coroots()) ]
....:     print coroots, highest_weight, multiplicity
....:
[1, 0, 0, 0, 0] (1, 0, 0, 0, 0) 2
[0, 1, 2, 3, 4] (8, 8, 7, 5, 2) 1


Note that I used a more complicated group where simple roots do not coincide with the simple coroot vectors as in SU(4).

You can get the coroot vector components from the inner product with the simple coroots, of course:

sage: B5 = WeylCharacterRing('B5',style='coroots')
sage: Rep = 2*B5(1,0,0,0,0) + B5(0,1,2,3,0)
B5(0,1,2,3,4)
sage: Rep.degree()    # dimension
3777283147
sage: for highest_weight, multiplicity in Rep:
....:     coroots = [ highest_weight.inner_product(coroot)
....:                 for coroot in list(B5.simple_coroots()) ]
....:     print coroots, highest_weight, multiplicity
....:
[1, 0, 0, 0, 0] (1, 0, 0, 0, 0) 2
[0, 1, 2, 3, 4] (8, 8, 7, 5, 2) 1


Note that I used a more complicated group where simple roots do not coincide with the simple coroot vectors as in SU(4).