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ConformalBlocks :: symmetrizedConformalBlockDivisor

symmetrizedConformalBlockDivisor -- computes the symmetrization of the first Chern class of a conformal block vector bundle

Synopsis

Description

This function implements the formula given in [Fakh] Corollary 3.6. It computes the symmetrization of the first Chern class of a conformal block vector bundle: $\sum_{S_n} c_1 V(\mathbf{g},l,(\lambda_{\sigma 1},...\lambda_{\sigma n}))$.

NEW in Version 2.1: Previously there was a separate, faster function to use in the case that $\lambda_1 = ... = \lambda_n$. However, now this function automatically checks for symmetry and uses the faster formula if applicable, so the user does not need to use two separate functions.

In the example below, we compute the symmetrization of the divisor class of the conformal block bundle $V(sl_4,1,(\omega_1,\omega_1,\omega_2,\omega_2,\omega_3,\omega_3))$.

i1 : sl_4 =simpleLieAlgebra("A",3);
i2 : V=conformalBlockVectorBundle(sl_4,1,{{1,0,0},{1,0,0},{0,1,0},{0,1,0},{0,0,1},{0,0,1}},0);
i3 : D=symmetrizedConformalBlockDivisor(V)

o3 = 288*B  + 288*B
          2        3

o3 : S_6-symmetric divisor on M-0-6-bar

Ways to use symmetrizedConformalBlockDivisor :

For the programmer

The object symmetrizedConformalBlockDivisor is a method function.