Representations of Hecke Algebras of General Linear Groups

Dipper, Richard; James, Gordon

doi:10.1112/plms/s3-52.1.20

Cited by 354 publications

(488 citation statements)

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“…The statement (2) is a well-known result; see e.g., [11]. We only give the proof of the statements (1) and (3).…”

Section: Jun Humentioning

confidence: 88%

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BMW algebra, quantized coordinate algebra and type 𝐶 Schur–Weyl duality

2011

Represent. Theory

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Abstract. We prove an integral version of the Schur-Weyl duality between the specialized Birman-Murakami-Wenzl algebra B n (−q 2m+1 , q) and the quantum algebra associated to the symplectic Lie algebra sp 2m . In particular, we deduce that this Schur-Weyl duality holds over arbitrary (commutative) ground rings, which answers a question of Lehrer and Zhang in the symplectic case. As a byproduct, we show that, as a Z[q, q −1 ]-algebra, the quantized coordinate algebra defined by Kashiwara (which he denoted by A Z q (g)) is isomorphic to the quantized coordinate algebra arising from a generalized Faddeev-Reshetikhin-Takhtajan construction.

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“…The statement (2) is a well-known result; see e.g., [11]. We only give the proof of the statements (1) and (3).…”

Section: Jun Humentioning

confidence: 88%

“…It plays an important role in the modular representation theory of finite groups of Lie type (cf. [11], [12], [24]). The significance of the above results lies in that it provides a bridge between the representation theory of type A quantum groups and of type A Hecke algebras at an integral level.…”

Section: Introductionmentioning

confidence: 99%

BMW algebra, quantized coordinate algebra and type 𝐶 Schur–Weyl duality

2011

Represent. Theory

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“…On the other hand, the adjointness is compatible with stable homomorphisms, see [DJ1]. So we have Hom(X, Dᾱ) ∼ = Hom(F (Dᾱ), F (Dᾱ)).…”

Section: Lemma the Module Gf (Dᾱ) Is Isomorphic To Dᾱ ⊕ P (ᾱ)mentioning

confidence: 93%

Representation type of Hecke algebras of type 𝐴

Erdmann

Nakano

2001

Trans. Amer. Math. Soc.

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“…Building upon results in [13] and [25] [18].) Not surprisingly, the dual canonical basis has no entirely elementary description.…”

Section: A Multigrading Of C[x] and Two Basesmentioning

confidence: 99%

Bitableaux and Zero Sets of Dual Canonical Basis Elements

Rhoades

Skandera

2011

Ann. Comb.

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Abstract. We state new results concerning the zero sets of polynomials belonging to the dual canonical basis of C[x 1,1 , . . . , x n,n ]. As an application, we show that this basis is related by a unitriangular transition matrix to the simpler bitableau basis popularized by Désarménien-Kung-Rota. It follows that spaces spanned by certain subsets of the dual canonical basis can be characterized in terms of products of matrix minors, or in terms of their common zero sets.

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Representations of Hecke Algebras of General Linear Groups

Cited by 354 publications

References 4 publications

BMW algebra, quantized coordinate algebra and type 𝐶 Schur–Weyl duality

BMW algebra, quantized coordinate algebra and type 𝐶 Schur–Weyl duality

Representation type of Hecke algebras of type 𝐴

Bitableaux and Zero Sets of Dual Canonical Basis Elements

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