Cohomological stratification of diagram algebras

Hartmann, R.; Koenig, Steffen; Paget, Rowena

doi:10.1007/s00208-009-0458-x

Cited by 31 publications

(46 citation statements)

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“…Diagram algebras share many structural features (such as being cellular), which raises the question of a general context where analogues of the Hemmer-Nakano theorem hold true. Such a general context has been developed in [29]. The class of cellularly stratified algebras defined there includes Brauer algebras (for δ = 0), their quantisations (the Birman-Murakami-Wenzl algebras), partition algebras (always assuming δ = 0) and presumably many or all other diagram algebras apart from degenerate cases.…”

Section: The Weyl Modules Formentioning

confidence: 99%

“…The class of cellularly stratified algebras defined there includes Brauer algebras (for δ = 0), their quantisations (the Birman-Murakami-Wenzl algebras), partition algebras (always assuming δ = 0) and presumably many or all other diagram algebras apart from degenerate cases. All of these algebras are made up, in a sense made precise in [39,29], from copies of various group algebras of symmetric groups, or their quantisations (Hecke algebras). A general result proved in [29] states that for a cellularly stratified algebra, validity of a Hemmer-Nakano theorem for these pieces always implies a Hemmer-Nakano theorem for the full algebra.…”

Section: The Weyl Modules Formentioning

confidence: 99%

“…All of these algebras are made up, in a sense made precise in [39,29], from copies of various group algebras of symmetric groups, or their quantisations (Hecke algebras). A general result proved in [29] states that for a cellularly stratified algebra, validity of a Hemmer-Nakano theorem for these pieces always implies a Hemmer-Nakano theorem for the full algebra.…”

Section: The Weyl Modules Formentioning

confidence: 99%

“…Other instances of Schur-Weyl dualities have been established for various classes of diagram algebras such as Brauer algebras, in [28] and more generally in [29]. [33]), or more generally of Schur algebras of diagram algebras (including BMW algebras and partition algebras, see [29]).…”

Section: Problem 1 Determine the Dominant Dimension Of Schur Algebramentioning

confidence: 99%

“…[33]), or more generally of Schur algebras of diagram algebras (including BMW algebras and partition algebras, see [29]). …”

Section: Problem 1 Determine the Dominant Dimension Of Schur Algebramentioning

confidence: 99%

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Dominant Dimension and Almost Relatively True Versions of Schur’s Theorem

Koenig

2010

Milan J. Math.

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Perhaps the most fundamental problems of representation theory are to classify and to describe irreducible (=simple) representations and to determine cohomology. It is crucial to develop techniques that allow to transfer information from some (known) cases to other (unknown) cases. A classical result of this kind, due to Schur, recently has been extended widely, and put into a general context. These modern 'relative' versions of Schur's result will be presented. Moreover, the theoretical background behind these results, and the crucial invariant controlling the existence and strength of such equivalences, will be explained, and illustrated by an explicit example. Finally, some open problems will be stated and discussed.

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Section: The Weyl Modules Formentioning

confidence: 99%

Section: The Weyl Modules Formentioning

confidence: 99%