Implement the Virasoro Algebra and it's representations.
The Virasoro Algebra is an infinite dimensional Lie algebra with generators L_n, n::integer satisfying
This is quite easy to implement with the "Physics" package:
What I'm having trouble with is defining vectors in my representation spaces. For example if I have a highest weight vector mu from which the entire representation is generated by the action of the Virasoro algebra.
I define mu by
where I'd like h to be the L_0 Eigenvalue. How do I define the action of the Virasoro algebra in mu? I tried
which works for L_0, but the L_n with n>0 do not map mu to 0.
What am I doing wrong.