Quantum Deformation of Classical Groups

Hayashi, Takahiro

doi:10.2977/prims/1195168856

Cited by 41 publications

(60 citation statements)

References 17 publications

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“…In [46] and [47], Oehms proved the pairing , 0 actually induces an A -algebra isomorphism S sy [29,Section 2], while the ideal generated by β X i,j − X i,j β for i, j ∈ I(2m, 2) in our paper is the same as the ideal generated by …”

Section: Jun Humentioning

confidence: 75%

“…In this section we shall give a proof of Theorem 1.5 in the case where m ≥ n. Henceforth, we shall assume that K is a field, and ζ is the image of q in K and m ≥ n. Note that, in this case, by [29…”

Section: As a Result This Is Still True If We Replace A By Any Commumentioning

confidence: 99%

“…Now we recall what Oehms called "generalized Faddeev-Reshetikhin-Takhtajan construction". The basic references are [23], [29] and [47]. We concentrate on the quantized type C case.…”

Section: Bmw Algebras and A Generalized Frt Constructionmentioning

confidence: 99%

“…Let d q ∈ A sy A (2m) be the central group-like element as defined in [47, (7)] and [29,Corollary 6.3]. By definition,…”

Section: Jun Humentioning

confidence: 99%

“…By [8, (10.2.5)] and [29,Section 4], the map ϕ C which sends each T i to β i and each E i to γ i for i = 1, 2, · · · , n − 1 can be naturally extended to a right action of…”

Section: Bmw Algebras and A Generalized Frt Constructionmentioning

confidence: 99%

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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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Section: Jun Humentioning

confidence: 75%

Section: As a Result This Is Still True If We Replace A By Any Commumentioning

confidence: 99%

“…Now we recall what Oehms called "generalized Faddeev-Reshetikhin-Takhtajan construction". The basic references are [23], [29] and [47]. We concentrate on the quantized type C case.…”

Section: Bmw Algebras and A Generalized Frt Constructionmentioning

confidence: 99%

“…Let d q ∈ A sy A (2m) be the central group-like element as defined in [47, (7)] and [29,Corollary 6.3]. By definition,…”

Section: Jun Humentioning

confidence: 99%

“…By [8, (10.2.5)] and [29,Section 4], the map ϕ C which sends each T i to β i and each E i to γ i for i = 1, 2, · · · , n − 1 can be naturally extended to a right action of…”

Section: Bmw Algebras and A Generalized Frt Constructionmentioning

confidence: 99%

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