On the Semisimplicity of the Brauer Centralizer Algebras

Doran, William F.; Wales, David B.; Hanlon, Philip J.

doi:10.1006/jabr.1998.7592

Cited by 62 publications

(97 citation statements)

References 7 publications

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“…The results of this section can be used to derive the next statement which is Theorem 3.3 of [3]. As in Theorem 8.5, the statement may be generalised to the setting where |λ| > |µ|.…”

Section: Semisimplicity Criteria For Brauer Algebrasmentioning

confidence: 92%

Specht modules and semisimplicity criteria for Brauer and Birman–Murakami–Wenzl algebras

Enyang

2007

J Algebr Comb

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Abstract. A construction of bases for cell modules of the Birman-Murakami-Wenzl (or B-M-W) algebra B n (q, r) by lifting bases for cell modules of B n−1 (q, r) is given. By iterating this procedure, we produce cellular bases for B-M-W algebras on which a large abelian subalgebra, generated by elements which generalise the Jucys-Murphy elements from the representation theory of the Iwahori-Hecke algebra of the symmetric group, acts triangularly. The triangular action of this abelian subalgebra is used to provide explicit criteria, in terms of the defining parameters q and r, for B-M-W algebras to be semisimple. The aforementioned constructions provide generalisations, to the algebras under consideration here, of certain results from the Specht module theory of the Iwahori-Hecke algebra of the symmetric group.

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“…The results of this section can be used to derive the next statement which is Theorem 3.3 of [3]. As in Theorem 8.5, the statement may be generalised to the setting where |λ| > |µ|.…”

Section: Semisimplicity Criteria For Brauer Algebrasmentioning

confidence: 92%

Specht modules and semisimplicity criteria for Brauer and Birman–Murakami–Wenzl algebras

Enyang

2007

J Algebr Comb

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“…The question rests on the semi-simplicity of B K (n), a matter which has not been fully resolved (cf. [HW89,DWH99]). …”

Section: Orthogonal and Symplectic Matricesmentioning

confidence: 99%

Linear functionals of eigenvalues of random matrices

Diaconis

Evans

2001

Trans. Amer. Math. Soc.

227

194

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Abstract. Let Mn be a random n × n unitary matrix with distribution given by Haar measure on the unitary group. Using explicit moment calculations, a general criterion is given for linear combinations of traces of powers of Mn to converge to a Gaussian limit as n → ∞. By Fourier analysis, this result leads to central limit theorems for the measure on the circle that places a unit mass at each of the eigenvalues of Mn. For example, the integral of this measure against a function with suitably decaying Fourier coefficients converges to a Gaussian limit without any normalisation. Known central limit theorems for the number of eigenvalues in a circular arc and the logarithm of the characteristic polynomial of Mn are also derived from the criterion. Similar results are sketched for Haar distributed orthogonal and symplectic matrices.

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“…removing) a box to its Young diagram. From [6] we have exact sequences 0 → ⊕ µ λ ∆ n−1 (µ) → res n ∆ n (λ) → ⊕ µ λ ∆ n−1 (µ) → 0, and…”

Section: We Have Natural Embeddings Of the Brauer Algebrasmentioning

confidence: 99%

On Brauer algebra simple modules over the complex field

Visscher

Martin

2016

Trans. Amer. Math. Soc.

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This is the accepted version of the paper.This version of the publication may differ from the final published version. Abstract. This paper gives two results on the simple modules for the Brauer algebra B n (δ) over the complex field. First we describe the module structure of the restriction of all simple B n (δ)-modules to B n−1 (δ). Second we give a new geometrical interpretation of Ram and Wenzl's construction of bases for 'δ-permissible' simple modules. Permanent

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On the Semisimplicity of the Brauer Centralizer Algebras

Cited by 62 publications

References 7 publications

Specht modules and semisimplicity criteria for Brauer and Birman–Murakami–Wenzl algebras

Specht modules and semisimplicity criteria for Brauer and Birman–Murakami–Wenzl algebras

Linear functionals of eigenvalues of random matrices

On Brauer algebra simple modules over the complex field

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