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Home > Vol 28, No 2 (2008)

Jun Hu

Beijing Institute of Technology Department of Applied Mathematics Beijing 100081 China

Let m, n\in \Bbb N. In this paper we study the right permutation action of the symmetric group \mathfrak S _{2 n} \mathfrak{S}_{2n} on the set of all the Brauer n-diagrams. A new basis for the free \Bbb Z-module \mathfrak B _n \mathfrak {B}_{n} spanned by these Brauer n-diagrams is constructed, which yields Specht filtrations for \mathfrak B _n \mathfrak {B}_{n} . For any 2 m-dimensional vector space V over a field of arbitrary characteristic, we give an explicit and characteristic-free description of the annihilator of the n-tensor space V ^{\otimes  n} in the Brauer algebra \mathfrak B _n( -2 m) \mathfrak {B}_{n}(-2m) . In particular, we show that it is a \mathfrak S _{2 n} \mathfrak{S}_{2n} -submodule of \mathfrak B _n( -2 m) \mathfrak {B}_{n}(-2m) .

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