Geodesic
Specht modules and semisimplicity criteria for Brauer and Birman-Murakami-Wenzl algebras.
Journal of Algebraic Combinatorics, Tome 26 (2007) no. 3, pp. 291-341.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Keywords: keywords birman-murakami-wenzl algebra, Brauer algebra, Specht module, cellular algebra, jucys-murphy operators 
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     author = {Enyang, John},
     title = {Specht modules and semisimplicity criteria for {Brauer} and {Birman-Murakami-Wenzl} algebras.},
     journal = {Journal of Algebraic Combinatorics},
     pages = {291--341},
     publisher = {mathdoc},
     volume = {26},
     number = {3},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2007__26_3_a4/}
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Enyang, John. Specht modules and semisimplicity criteria for Brauer and Birman-Murakami-Wenzl algebras.. Journal of Algebraic Combinatorics, Tome 26 (2007) no. 3, pp. 291-341. http://geodesic.mathdoc.fr/item/JAC_2007__26_3_a4/