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Gabriel, Patrick

doi:10.24033/bsmf.1583

Cited by 1,262 publications

(891 citation statements)

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“…The general construction of such an algebra starting from an additive category can be traced back to [21,Chap. II], and we describe it in our particular case.…”

Section: Definitions Of Globally Defined Mackey Functors and Preliminmentioning

confidence: 99%

Stratifications and Mackey Functors II: Globally Defined Mackey Functors

Webb¹

2010

J K-Theor

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Abstract. We describe structural properties of globally defined Mackey functors related to the stratification theory of algebras. We show that over a field of characteristic zero they form a highest weight category and we also determine precisely when this category is semisimple. This approach is used to show that the Cartan matrix is often symmetric and non-singular, and we are able to compute finite parts of it in some instances. We also develop a theory of vertices of globally defined Mackey functors in the spirit of group representation theory, as well as giving information about extensions between simple functors.

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“…The general construction of such an algebra starting from an additive category can be traced back to [21,Chap. II], and we describe it in our particular case.…”

Section: Definitions Of Globally Defined Mackey Functors and Preliminmentioning

confidence: 99%

Stratifications and Mackey Functors II: Globally Defined Mackey Functors

Webb¹

2010

J K-Theor

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“…The categories W d (λ)-mod and H d (λ)-mod thus give two different realizations of a natural quotient of the category O d (λ) in the general sense of [Gab,§III.1], the respective quotient functors being the Whittaker functor V and the functor Hom g (P ⊗ V ⊗d , ? ).…”

Section: Introductionmentioning

confidence: 99%

Schur–Weyl duality for higher levels

Brundan

Kleshchev

2008

Sel. math., New ser.

190

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Abstract. We extend Schur-Weyl duality to an arbitrary level l ≥ 1, level one recovering the classical duality between the symmetric and general linear groups. In general, the symmetric group is replaced by the degenerate cyclotomic Hecke algebra over C parametrized by a dominant weight of level l for the root system of type A∞. As an application, we prove that the degenerate analogue of the quasi-hereditary cover of the cyclotomic Hecke algebra constructed by Dipper, James and Mathas is Morita equivalent to certain blocks of parabolic category O for the general linear Lie algebra.

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“…The Gabriel functor ring (see [5] induces an equivalence between Fl(R) and the quotient category of Mod(R) corresponding to a certain hereditary torsion theory σ of Mod(R). Since the functor H is naturally isomorphic to the inclusion functor Fl(R) → Mod(R) then σ is a hereditary torsion theory of Mod(R) such that the σ-closed modules are precisely the flat right R-modules.…”

Section: Preliminary Results On Panoramic Ringsmentioning

confidence: 99%