The Decomposition Of The Fourth Tensor Product Of The Natural Representation Of Lie Super Algebra P(n)

We analyzed the decomposition of tensor product representation of Lie superalge-bra p(n)according to the paper of D.Moon.In his paper,Moon analyzed the decom-position of second and third tensor products.But the fourth tensor products is more complicated.We used GAP to do calculation in this situation.According to the idea of Schur-Weyl duality,we analyzed the centralizer algebra of p(n)using the theory of cellular algebra.We can decide the semisimplify of Ak when k is small.