Multiplicity function for tensor powers of modules of the An algebra

@article{Kulish2012MultiplicityFF,
  title={Multiplicity function for tensor powers of modules of the An algebra},
  author={Petr P. Kulish and Vladimir D. Lyakhovsky and O. V. Postnova},
  journal={Theoretical and Mathematical Physics},
  year={2012},
  volume={171},
  pages={666-674}
}
We consider the decomposition of the pth tensor power of the module $$L^{\omega _1 }$$ over the algebra An into irreducible modules, $$(L^{\omega _1 } )^{ \otimes p} = \sum\nolimits_v {m(v,p)L^v }$$. This problem occurs, for example, in finding the spectrum of an invariant Hamiltonian of a spin chain with p nodes. To solve the problem, we propose using the Weyl symmetry properties. For constructing the coefficients m(ν, p) as functions of p, we develop an algorithm applicable to powers of an… CONTINUE READING