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

Synopsis

Usage:

conformalBlockRank(V)
Inputs:
- V, an instance of the type ConformalBlockVectorBundle,
Outputs:
- r, an integer,

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 a method function.