The blocks of the Brauer algebra in characteristic zero

Cox, Anton; Visscher, Maud De; Martin, Paul

doi:10.1090/s1088-4165-09-00305-7

Cited by 59 publications

(130 citation statements)

References 29 publications

Supporting

Mentioning

128

Contrasting

Order By: Relevance

“…Via it, we classify the blocks of cyclotomic NW and cyclotomic BMW algebras over the field κ under the additional Assumption 4.1. This generalizes Cox-De Visscher-Martin's work on Brauer algebras and our work on BMW algebras in [7,35]. Via such results, we determine certain zero factors of the Gram determinant associated to each cell module for cyclotomic NW algebras and cyclotomic BMW algebras.…”

Section: Introductionsupporting

confidence: 62%

“…Such algebras can be considered as the q-analog of the Brauer algebras in [6]. Motivated by Cox, De Visscher and Martin's work on the blocks of Brauer algebras in characteristic zero [7], we have classified the blocks of BMW algebras over the field κ which contains invertible parameters r and q such that o(q 2 ), the order of q 2 , is large enough and char(κ), the characteristic of the field κ, is not equal to 2 [35]. As a by-product, we determine certain zero divisors of the Gram determinant associated to each cell module for BMW algebras.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Non-vanishing Gram determinants for cyclotomic Nazarov–Wenzl and Birman–Murakami–Wenzl algebras

Rui

2011

Journal of Algebra

View full text Add to dashboard Cite

show abstract

Section: Introductionsupporting

confidence: 62%

Section: Introductionmentioning

confidence: 99%

Non-vanishing Gram determinants for cyclotomic Nazarov–Wenzl and Birman–Murakami–Wenzl algebras

Rui

2011

Journal of Algebra

View full text Add to dashboard Cite

show abstract

“…For any δ ∈ k one has the Brauer algebra B r (δ); see, e.g. [4,5,21,40] or [9] for a definition. This also makes sense for δ an integer, since we can replace that integer by its natural image in k. Let E ⊗r be the r -fold tensor power of E. Then we have natural homomorphisms kSym r → End GL n (E ⊗r ) and B r (−n) → End Sp n (E ⊗r ).…”

Section: The Brauer Algebra and The Symplectic Schur Algebramentioning

confidence: 99%

The Brauer algebra and the symplectic Schur algebra

Donkin

Tange

2009

Math. Z.

View full text Add to dashboard Cite

Let k be an algebraically closed field of characteristic p > 0, let m, r be integers with m ≥ 1, r ≥ 0 and m ≥ r and let S 0 (2m, r ) be the symplectic Schur algebra over k as introduced by the first author. We introduce the symplectic Schur functor, derive some basic properties of it and relate this to work of Hartmann and Paget. We do the same for the orthogonal Schur algebra. We give a modified Jantzen sum formula and a block result for the symplectic Schur algebra under the assumption that r and the residue of 2m mod p are small relative to p. From this we deduce a block result for the orthogonal Schur algebra under similar assumptions. We also show that, in general, the block relations of the Brauer algebra and the symplectic and orthogonal Schur algebra are the same. Finally, we deduce from the previous results a new proof of the description of the blocks of the Brauer algebra in characteristic 0 as obtained by Cox, De Visscher and Martin.

show abstract

“…Via the partial order P we, in particular, obtain information on the decomposition numbers of the Brauer algebra B δ (n), that is, on the composition factors of standard modules. It should be pointed out that further information on decomposition numbers of Brauer algebras over fields of characteristic 0 can, for instance, be found in [8].…”

Section: Brauer Algebrasmentioning

confidence: 99%

Quasi-hereditary structure of twisted split category algebras revisited

Boltje

Danz

2015

Journal of Algebra

View full text Add to dashboard Cite

Available online xxxx Communicated by Michel Broué MSC: 16G10 20M17 19A22 Keywords: Split category Regular monoid Quasi-hereditary algebra Highest weight category Biset functor Brauer algebraLet k be a field of characteristic 0, let C be a finite split category, let α be a 2-cocycle of C with values in the multiplicative group of k, and consider the resulting twisted category algebra A := k α C. Several interesting algebras arise that way, for instance, the Brauer algebra. Moreover, the category of biset functors over k is equivalent to a module category over a condensed algebra εAε, for an idempotent ε of A. In [2] the authors proved that A is quasi-hereditary (with respect to an explicit partial order on the set of irreducible modules), and standard modules were given explicitly. Here, we improve the partial order by introducing a coarser order P leading to the same results on A, but which allows to pass the quasi-heredity result to the condensed algebra εAε describing biset functors, thereby giving a different proof of a quasi-heredity result of Webb, see [21]. The new partial order P has not been considered before, even in the special cases, and we evaluate it explicitly for the case of biset functors and the Brauer algebra. It also puts further restrictions on the possible composition factors of standard modules.

show abstract

The blocks of the Brauer algebra in characteristic zero

Abstract: Abstract. 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.

Cited by 59 publications

References 29 publications

Non-vanishing Gram determinants for cyclotomic Nazarov–Wenzl and Birman–Murakami–Wenzl algebras

Non-vanishing Gram determinants for cyclotomic Nazarov–Wenzl and Birman–Murakami–Wenzl algebras

The Brauer algebra and the symplectic Schur algebra

Quasi-hereditary structure of twisted split category algebras revisited

Contact Info

Product

Resources

About