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論文
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Ito, Tatsuro ; Terwilliger, Paul
概要:
金沢大学大学院自然科学研究科計算科学<br />金沢大学理学部<br />Let double-struck K denote an algebraically closed field and let q denote a nonzero
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scalar in double-struck K that is not a root of unity. Let V denote a vector space over double-struck K with finite positive dimension and let A, A* denote a tridiagonal pair on V. Let θ0, θ1,..., θd (resp. θ0*, θ1*,..., θd*) denote a standard ordering of the eigenvalues of A (resp. A*). We assume there exist nonzero scalars a, a* in double-struck K such that θi = aq 2i-d and θi* = a*qd-2i for 0 ≤ i ≤ d. We display two irreducible Uq(sl2)-module structures on V and discuss how these are related to the actions of A and A*. © 2006 Springer Science + Business Media, LLC.
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| 2.
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論文
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Ito, Tatsuro ; Terwilliger, P.
概要:
金沢大学大学院自然科学研究科計算科学<br />Recently, Hartwig and the second author found a presentation for the three-point 2 loop algebra
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via generators and relations. To obtain this presentation they defined an algebra by generators and relations, and displayed an isomorphism from to the three-point 2 loop algebra. We introduce a quantum analog of which we call q. We define q via generators and relations. We show how q is related to the quantum group Uq(2), the Uq(2) loop algebra, and the positive part of [image omitted]. We describe the finite dimensional irreducible q-modules under the assumption that q is not a root of 1, and the underlying field is algebraically closed.
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論文
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Ito, Tatsuro ; Terwilliger, Paul ; Weng, Chih-wen
概要:
金沢大学理学部<br />We show that the quantum algebra Uq(sl2) has a presentation with generators x±1,y, z and relations xx-1 = x
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-1x = 1, qxy - q-1yx/q - q-1 = 1, qyz - q-1zy/q - q-1 = 1, qzx - q-1xz/q - q-1 = 1. We call this the equitable presentation. We show that y (respectively z) is not invertible in Uq(sl2) by displaying an infinite-dimensional Uq(sl2)-module that contains a nonzero null vector for y(respectively z). We consider finite-dimensional Uq(sl2)-modules under the assumption that q is not a root of 1 and char (K) ≠ 2, where K is the underlying field. We show that y and z are invertible on each finite-dimensional Uq(sl2)-module. We display a linear operator Ω that acts on finite-dimensional Uq (sl2)-modules, and satisfies Ω-1xΩ = y, Ω-1yΩ = z, Ω-1zΩ = x on these modules. We define Ω using the q-exponential function. © 2005 elsevier Inc. All rigths reserved.
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| 4.
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論文
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Ito, Tatsuro ; Terwilliger, Paul M.
概要:
Let double-struck K denote an algebraically closed field and let q denote a nonzero scalar in double-struck K that is no
…
t a root of unity. Let V denote a vector space over double-struck K with finite positive dimension and let A, A* denote a tridiagonal pair on V. Let θ0, θ1,..., θd (resp. θ0*, θ1*,..., θd*) denote a standard ordering of the eigenvalues of A (resp. A*). We assume there exist nonzero scalars a, a* in double-struck K such that θi = aq 2i-d and θi* = a*qd-2i for 0 ≤ i ≤ d. We display two irreducible Uq(sl2)-module structures on V and discuss how these are related to the actions of A and A*. © 2006 Springer Science + Business Media, LLC.
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