# On Brauer algebra simple modules over the complex field

@article{Visscher2012OnBA, title={On Brauer algebra simple modules over the complex field}, author={Maud De Visscher and Paul Purdon Martin}, journal={Transactions of the American Mathematical Society}, year={2012}, volume={369}, pages={1579-1609} }

This paper gives two results on the simple modules for the Brauer algebra Bn(δ) over the complex field. First we describe the module structure of the restriction of all simple Bn(δ)-modules to Bn−1(δ). Second we give a new geometrical interpretation of Ram and Wenzl’s construction of bases for ‘δ-permissible’ simple modules.

## 6 Citations

### The Structure of Simple Modules of Birman-Murakami-Wenzl Algebras

- Mathematics
- 2015

We study the restriction of simple modules of Birman-Murakami-Wenzl algebras with being not a root of 1. Precisely, we study the module structure for the restriction of to and describe the socle and…

### Simple modules for the partition algebra and monotone convergence of Kronecker coefficients

- Mathematics
- 2016

We construct bases of the simple modules for partition algebras which are indexed by paths in an alcove geometry. This allows us to give a concrete interpretation (and new proof) of the monotone…

### The cellular second fundamental theorem of invariant theory for classical groups

- Mathematics
- 2016

We prove that the centralizer algebras of the symplectic and orthogonal group acting on tensor space are cellular algebras over the integers. We do this by providing an axiomatic framework for…

### The Structure of Simple Modules of Birman-Murakami-Wenzl Algebras

- Mathematics
- 2015

Classical Schur-Weyl duality relates the representations of the symmetric and general linear groups via their actions on tensor space. Brauer [1] introduced a class of algebras called Brauer algebras…

## References

SHOWING 1-10 OF 22 REFERENCES

### The decomposition matrices of the Brauer algebra over the complex field

- Mathematics
- 2009

The Brauer algebra was introduced by R. Brauer in 1937 as a tool in invariant theory. The problem of determining the Cartan decomposition matrix of the Brauer algebra over the complex field has…

### Young modules and filtration multiplicities for Brauer algebras

- Mathematics
- 2006

We define permutation modules and Young modules for the Brauer algebra Bk(r,δ), and show that if the characteristic of the field k is neither 2 nor 3 then every permutation module is a sum of Young…

### A geometric characterisation of the blocks of the Brauer algebra

- Mathematics
- 2009

We give a geometric description of the blocks of the Brauer algebra in characteristic zero as orbits of the Weyl group of type Dn. We show how the corresponding affine Weyl group controls the block…

### The blocks of the Brauer algebra in characteristic zero

- Mathematics
- 2006

We determine the blocks of the Brauer algebra in characteristic zero. We also give information on the submodule structure of standard modules for this algebra.

### A GRAPHICAL DESCRIPTION OF (Dn,An−1) KAZHDAN–LUSZTIG POLYNOMIALS

- MathematicsGlasgow Mathematical Journal
- 2012

Abstract We give an easy diagrammatical description of the parabolic Kazhdan–Lusztig polynomials for the Weyl group Wn of type Dn with parabolic subgroup of type An and consequently an explicit…

### Branching Rules for Symmetric Groups and Applications

- Mathematics
- 1998

Let F be an arbitrary field of characteristic p ≥ 0, and Σ n be the symmetric group on n letters. We shall discuss finite-dimensional representations of Σ n over F or, equivalently,…