Specht filtrations and tensor spaces for the Brauer algebra

2006/04/26 by Jun Hu, Hu, Jun
Mathematics · #20C20 #20G05 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.math/0604577

openalex publication_date 2006/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let m, n∈\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^{⊗ 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).

Citations

• Tensor Product Representations of General Linear Groups and Their Connections with Brauer Algebras

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