This function implements the formula given in [Fakh] Corollary 3.5 for computing the degree of a conformal block vector bundle V on M0,4.
The first line of the example below shows that the conformal block bundle V(sl3,1,(ω1,ω1,ω2,ω2)) has degree 1 on M0,4 ≅ℙ1. The second line shows that this vector bundle is a line bundle. Hence, V(sl3,1,(ω1,ω1,ω2,ω2)) is isomorphic to O(1).
i1 : needsPackage("LieTypes") o1 = LieTypes o1 : Package |
i2 : sl_3 = simpleLieAlgebra("A",2); |
i3 : V=conformalBlockVectorBundle(sl_3,1,{{1,0},{1,0},{0,1},{0,1}},0); |
i4 : conformalBlockDegreeM04bar(V) o4 = 1 |
i5 : conformalBlockRank(V) o5 = 1 |