# conformalBlockRank -- computes the rank of the conformal block vector bundle

## Description

This function uses propagation and factorization to recursively compute ranks in terms of the ranks on $\bar{M}_{0,3}$. These are determined by the so-called fusion rules and are computed via the function fusionCoefficient in the LieTypes package. See [Beauville] for details on these topics.

In the example below we compute the rank of the conformal block bundle $V(sl_3,2,(\omega_1,\omega_1,\omega_2,\omega_2))$.

 i1 : sl_3=simpleLieAlgebra("A",2); i2 : V=conformalBlockVectorBundle(sl_3,2,{{1,0},{1,0},{0,1},{0,1}},0) o2 = V o2 : Conformal block vector bundle on M-0-4-bar i3 : conformalBlockRank(V) o3 = 2

## Ways to use conformalBlockRank :

• "conformalBlockRank(ConformalBlockVectorBundle)"

## For the programmer

The object conformalBlockRank is .