1 | initial version |
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).
2 | No.2 Revision |
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).
3 | No.3 Revision |
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).