Abstract
The purpose of this paper is to find a new way to prove the n! conjecture for particular partitions. The idea is to construct a monomial and explicit basis for the space M μ . We succeed completely for hook-shaped partitions, i.e., μ=( K+1,1 L ). We are able to exhibit a basis and to verify that its cardinality is indeed n!, that it is linearly independent and that it spans M μ . We derive from this study an explicit and simple basis for I μ , the annihilator ideal of Δ μ . This method is also successful for giving directly a basis for the homogeneous subspace of M μ consisting of elements of 0 x-degree.
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