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Twisted Quantum Affine Algebras
, 1996
"... Quantum affine algebras are one of the most important classes of quantum groups. Their finitedimensional representations lead to solutions of the quantum Yang– Baxter equation which are trigonometric functions of the spectral parameter (see [7], Sect. 12.5 B) and are thus related to various types o ..."
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Cited by 18 (1 self)
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Quantum affine algebras are one of the most important classes of quantum groups. Their finitedimensional representations lead to solutions of the quantum Yang– Baxter equation which are trigonometric functions of the spectral parameter (see [7], Sect. 12.5 B) and are thus related to various types
On the Comultiplication in Quantum Affine Algebras
, 1999
"... We express the comultiplication of the generators in Drinfelds second realization of the quantum affine algebra Uq ( ˆ sl2), induced by the comultiplication of the generators in the DrinfeldJimbo realization of Uq ( ˆ sl2) in terms of generating functions. Then we find explicit expressions for th ..."
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We express the comultiplication of the generators in Drinfelds second realization of the quantum affine algebra Uq ( ˆ sl2), induced by the comultiplication of the generators in the DrinfeldJimbo realization of Uq ( ˆ sl2) in terms of generating functions. Then we find explicit expressions
On Drinfeld Realization Of Quantum Affine Algebras
, 1996
"... We provide a direct proof of the Drinfeld realization for the quantum affine algebras. 1. ..."
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Cited by 37 (9 self)
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We provide a direct proof of the Drinfeld realization for the quantum affine algebras. 1.
Cluster algebras and quantum affine algebras
, 2009
"... Let C be the category of finitedimensional representations of a quantum affine algebra Uq(̂g) of simplylaced type. We introduce certain monoidal subcategories Cℓ (ℓ ∈ N) of C ..."
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Cited by 71 (10 self)
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Let C be the category of finitedimensional representations of a quantum affine algebra Uq(̂g) of simplylaced type. We introduce certain monoidal subcategories Cℓ (ℓ ∈ N) of C
Quantum affine algebras and their representations, preprint
, 1994
"... Abstract. We prove a highest weight classification of the finitedimensional irreducible representations of a quantum affine algebra, in the spirit of Cartan’s classification of the finitedimensional irreducible representations of complex simple Lie algebras in terms of dominant integral weights. W ..."
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Cited by 89 (14 self)
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Abstract. We prove a highest weight classification of the finitedimensional irreducible representations of a quantum affine algebra, in the spirit of Cartan’s classification of the finitedimensional irreducible representations of complex simple Lie algebras in terms of dominant integral weights
On quantum shuffle and quantum affine algebras
, 2001
"... A construction of the quantum affine algebra Uq(ˆg) is given in two steps. We explain how to obtain the algebra from its positive Borel subalgebra Uq(b +), using a construction similar to Drinfeld’s quantum double. Then we show how the positive Borel subalgebra can be constructed with quantum shuffl ..."
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Cited by 9 (0 self)
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A construction of the quantum affine algebra Uq(ˆg) is given in two steps. We explain how to obtain the algebra from its positive Borel subalgebra Uq(b +), using a construction similar to Drinfeld’s quantum double. Then we show how the positive Borel subalgebra can be constructed with quantum
Representations of Quantum Affine Algebras
 Selecta Math (NS
, 1995
"... this paper by an expression "a Umodule" we will always understand "a Umodule from the category C" ..."
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Cited by 12 (2 self)
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this paper by an expression "a Umodule" we will always understand "a Umodule from the category C"
Coideal subalgebras in quantum affine algebras
, 2003
"... We introduce two subalgebras in the type A quantum affine algebra which are coideals with respect to the Hopf algebra structure. In the classical limit q → 1 each subalgebra specializes to the enveloping algebra U(k), where k is a fixed point subalgebra of the loop algebra gl N[λ,λ −1] with respect ..."
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Cited by 32 (4 self)
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We introduce two subalgebras in the type A quantum affine algebra which are coideals with respect to the Hopf algebra structure. In the classical limit q → 1 each subalgebra specializes to the enveloping algebra U(k), where k is a fixed point subalgebra of the loop algebra gl N[λ,λ −1] with respect
SOLITONS, BOUNDARIES, AND QUANTUM AFFINE ALGEBRAS
, 2002
"... Abstract. This is a condensed writeup of a talk delivered at the Ramanujan International Symposium on KacMoody Lie algebras and Applications in Chennai in January 2002. The talk introduces special coideal subalgebras of quantum affine algebras which appear in physics when solitons are restricted t ..."
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Cited by 1 (0 self)
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Abstract. This is a condensed writeup of a talk delivered at the Ramanujan International Symposium on KacMoody Lie algebras and Applications in Chennai in January 2002. The talk introduces special coideal subalgebras of quantum affine algebras which appear in physics when solitons are restricted
Results 1  10
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10,873