Specht filtrations and tensor spaces for the Brauer algebra

Details Specht filtrations and tensor spaces for the Brauer algebra Specht filtrations and tensor spaces for the Brauer algebra

2006-04-26

arxiv.org/abs/math/0604577v2

Mathematics

Representation Theory

Scientific paper

Let $m, n\in{\mathbb N}$. In this paper we study the right permutation action of the symmetric group ${\mathfrak S}_{2n}$ on the set of all the Brauer $n$-diagrams. A new basis for the free ${\mathbb Z}$-module ${\mathfrak B}_n$ spanned by these Brauer $n$-diagrams is constructed, which yields Specht filtrations for ${\mathfrak B}_n$. For any $2m$-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 ${\mathfrak B}_n(-2m)$. In particular, we show that it is a ${\mathfrak S}_{2n}$-submodule of ${\mathfrak B}_n(-2m)$.

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