A cell filtration of mixed tensor space

2014/08/28 by Friederike Stoll, Mathias Werth, Stoll, Friederike +1 · 1 citation
Mathematics · #16D20 #16G30 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT) #math.RT #msc:16D20 #msc:16G30

paper · pdf · doi:10.48550/arxiv.1408.6720

arxiv created 2014/08/28 · openalex publication_date 2014/08/28 · arxiv updated 2014/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a cellular basis of the walled Brauer algebra which has similar properties as the Murphy basis of the group algebra of the symmetric group. In particular, the restriction of a cell module to a certain subalgebra can be easily described via this basis. Furthermore, the mixed tensor space possesses a filtration by cell modules -- although not by cell modules of the walled Brauer algebra itself, but by cell modules of its image in the algebra of endomorphisms of mixed tensor space.

Citations

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

Cited by

• Bimodule structure of the mixed tensor product over Uqsℓ(2|1) and quantum walled Brauer algebra

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