Young's Orthogonal Form for Brauer's Centralizer Algebra

Nazarov, Maxim

doi:10.1006/jabr.1996.0195

Cited by 100 publications

(173 citation statements)

References 18 publications

Supporting

Mentioning

172

Contrasting

Order By: Relevance

“…In [10], M. Nazarov made use of operators x i with are related to the L i defined above by For integers j, k with 1 ≤ j, k ≤ n, we define the elements L In particular, L…”

Section: Jucys-murphy Operators For the Brauer Algebrasmentioning

confidence: 99%

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

Enyang

2007

J Algebr Comb

View full text Add to dashboard Cite

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.

show abstract

“…In [10], M. Nazarov made use of operators x i with are related to the L i defined above by For integers j, k with 1 ≤ j, k ≤ n, we define the elements L In particular, L…”

Section: Jucys-murphy Operators For the Brauer Algebrasmentioning

confidence: 99%

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

Enyang

2007

J Algebr Comb

View full text Add to dashboard Cite

show abstract

“…We give below an alternative proof for this formula. Our method is inspired by the Nazarov computation of the matrix elements of the action of the hook generators on the canonical basis of the irreducible representations of Brauer algebras [14]. Here we work with scalar field k = Q(s, α), hence we have that all the quantum dimensions λ are invertible.…”

Section: Quantum Dimensionmentioning

confidence: 99%

Skein construction of idempotents in Birman-Murakami-Wenzl algebras

Beliakova¹,

Blanchet²

2001

Mathematische Annalen

View full text Add to dashboard Cite

Abstract. We give skein theoretic formulas for minimal idempotents in the Birman-Murakami-Wenzl algebras. These formulas are then applied to derive various known results needed in the construction of quantum invariants and modular categories. In particular, an elementary proof of the Wenzl formula for quantum dimensions is given. This proof does not use the representation theory of quantum groups and the character formulas.

show abstract

“…This construction could be regarded as a cellular analogue of the constructions in [34][35][36]38]. Each of the examples that we want to study is a tower (A n ) n≥0 of algebras that generically is obtained from another tower (Q n ) n≥0 by repeated Jones basic constructions.…”

Section: Introductionmentioning

confidence: 99%