Blocks of Birman-Murakami-Wenzl Algebras

The Representations of Cyclotomic BMW Algebras, II

“…We remark that we will use our formulae on Gram determinants to determine the block theory on B r,n provided that the corresponding Ariki-Koike algebra is semisimple over a field with characteristic different from 2. This generalizes our work on BMW algebras in [19]. Details will be given in Rui and Si (Non-Vanishing Gram Determinants for Cyclotomic NW and BMW Algebras, preprint).…”

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

“…Rui and Si classified the blocks of BMW algebras with ( ) > [13]. Based on this result, it was shown in [6] that two simple B ( , )-modules , and ℓ, are in the same block if and only if ( ) ∈ ( ).…”

“…Note that res is exact functor and ind is right exact functor. By standard arguments in [12, Section 6], Rui and Si defined the exact functor F : mod-B ( , ) → mod-B −2 ( , ) and right exact functor G −2 : mod-B −2 ( , ) → mod-B ( , ) in [13], which satisfy…”

Decomposition matrices of Birman–Murakami–Wenzl algebras

“…In non-semisimple cases and κ = C, by Ariki's result on decomposition numbers of Hecke algebras in [4], decomposition numbers of B r (̺, q) are determined by the values of certain inverse Kazhdan-Lusztig polynomials at q = 1 associated to some extended affine Weyl groups of type A. If ̺ ∈ {q a , −q a } for some a ∈ Z and if q 2 is not a root of unity, Rui and Si classified blocks of B r (̺, q) over κ [22]. Via such results together with Martin's arguments on the decomposition matrices of Brauer algebras over C in [19], Xu showed that B r (̺, q) is multiplicity-free over C [31].…”