The uniqueness theorem for the universal R-matrix

Khoroshkin, S.; Tolstoy, V. N.

doi:10.1007/bf00402899

Cited by 77 publications

(132 citation statements)

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“…Taking into account that the character α(h) (equation (2.2)) can be written in the form 9) it is easy to figure out that operator S has to intertwine the representations T α ⊗ T β and…”

Section: Exchange Operatormentioning

confidence: 99%

“…The problem of constructing solutions to the YBE was thoroughly analyzed in the works of Drinfeld [3,4], Jimbo [5] and many others. In the most studied case of the quantum affine Lie (super)algebras the universal R-matrix was constructed in works of Rosso [6], Kirillov and Reshetikhin [7] and Khoroshkin and Tolstoy [8,9]. The interrelation of YBE with the representation theory was elucidated by Kulish, Reshetikhin and Sklyanin [10,11], who studied solutions of YBE for finite dimensional representations of the GL(N, C) group.…”

Section: Introductionmentioning

confidence: 99%

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R-Matrix and Baxter Q-Operators for the Noncompact SL(N,C) Invariant Spin Chain

Derkachov¹

2006

SIGMA

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Section: Exchange Operatormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

R-Matrix and Baxter Q-Operators for the Noncompact SL(N,C) Invariant Spin Chain

Derkachov¹

2006

SIGMA

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“…1) В нашей конструкции, в отличие от описаной в [5], в построении базиса Картана-Вейля ис-пользуются q-коммутаторы вместо q −1 -коммутаторов.…”

Section: реализации алгебрыunclassified

“…Алгебра U q (A (2) 2 ) также изучалась и с алгебраической точки зрения. В рабо-те [5] был построен базис Картана-Вейля для адгебры U q (A (2) 2 ) и универсальная R-матрица была выписана через бесконечные произведения элементов этого ба-зиса. Классификация конечномерных представлений алгебры U q (A (2) 2 ) была по-лучена в работе [6] в терминах полиномов Дринфельда.…”

Section: Introductionunclassified

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Три реализации квантовой аффинной алгебры $U_q(A_2^{(2)})$

Шапиро¹,

Shapiro²

2010

ТМФ

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On Harmonic Elements for Semi-simple Lie Algebras

Caldero

2002

Advances in Mathematics

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Let g be a semi-simple complex Lie algebra and g=n − À h À n its triangular decomposition. Let U(g), resp. U q (g), be its enveloping algebra, resp. its quantized enveloping algebra. This article gives a quantum approach to the combinatorics of (classical) harmonic elements and Kostant's generalized exponents for g. A quantum analogue of the space of harmonic elements has been given by A. Joseph and G. Letzter (1994, Amer. J. Math. 116, 127-177). On the one hand, we give specialization results concerning harmonic elements, central elements of U q (g), and the decomposition of Joseph and Letzter (cited above). For g=sl n+1 , we describe the specialization of quantum harmonic space in the N-filtered algebra U(sl n+1 ) as the materialization of a theorem of A. Lascoux et al. (1995, Lett. Math. Phys. 35, 359-374). This enables us to study a Joseph-Letzter decomposition in the algebra U(sl n+1 ). On the other hand, we prove that highest weight harmonic elements can be calculated in terms of the dual of Lusztig's canonical basis. In the simply laced case, we parametrize a basis of n-invariants of minimal primitive quotients by the set C 0 of integral points of a convex cone. © 2002 Elsevier Science (USA) Key Words: quantum groups; enveloping algebras; canonical basis; harmonic space.0. INTRODUCTION 0.1. Let V be a complex finite dimensional space and G a Lie subgroup of GL(V). Assume that V is completely reducible as a G-module. Then G acts semi-simply on the symmetric C-algebra S(V). Let J be the ideal generated by the non-constant homogeneous G-invariant elements of S(V). Let V g be the dual of V. There exists a natural non-degenerate duality between S(V) and S(V) be the orthogonal of J and H g be the space of G-harmonic polynomials of V.

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The uniqueness theorem for the universal R-matrix

Cited by 77 publications

References 9 publications

R-Matrix and Baxter Q-Operators for the Noncompact SL(N,C) Invariant Spin Chain

R-Matrix and Baxter Q-Operators for the Noncompact SL(N,C) Invariant Spin Chain

Три реализации квантовой аффинной алгебры $U_q(A_2^{(2)})$

On Harmonic Elements for Semi-simple Lie Algebras

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