scientific article; zbMATH DE number 1131864

zbMath0891.17013arXivq-alg/9609031MaRDI QIDQ4382854

Vyjayanthi Chari, Andrew Pressley

Publication date: 23 March 1998

Full work available at URL: https://arxiv.org/abs/q-alg/9609031

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zbMATH Keywords

irreducible representationsaffine Lie algebrahighest weightsquantized universal enveloping algebraFrobenius kernel

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67)

Related Items (27)

TWO DESCRIPTIONS OF THE QUANTUM AFFINE ALGEBRA U_v() VIA HALL ALGEBRA APPROACH ⋮ The \(t\)-analogs of \(q\)-characters at roots of unity for quantum affine algebras and beyond ⋮ Representations of \(U_q(L\mathfrak{sl}_2)\) at roots of unity and generalised cluster algebras ⋮ A functional model for the tensor product of level \(1\) highest and level \(-1\) lowest modules for the quantum affine algebra \(U_q(\widetilde{\mathfrak{sl}}_2)\) ⋮ Integral bases for the universal enveloping algebras of Cartan map superalgebras ⋮ An integral basis for the universal enveloping algebra of the Onsager algebra ⋮ Unnamed Item ⋮ Geometry of the analytic loop group ⋮ Duality of Lusztig and RTT integral forms of \(U_{\boldsymbol{v}}(L\mathfrak{sl}_n)\) ⋮ Unnamed Item ⋮ Integral bases for the universal enveloping algebras of map superalgebras ⋮ An algebraic characterization of the affine canonical basis ⋮ Finite-dimensional representations of hyper loop algebras over non-algebraically closed fields ⋮ Representations of Uεres(sl2) via restricted q-Fock spaces ⋮ A new aspect of representations of \(U_q(s\hat l_2)\) -- root of unity case ⋮ Loop symmetry of integrable vertex models at roots of unity ⋮ Quivers and Representations ⋮ PBWD bases and shuffle algebra realizations for \(U_v(L\mathfrak{sl}_n)\), \(U_{v_1,v_2} (L\mathfrak{sl}_n)\), \(U_v (L\mathfrak{sl}(m|n))\) and their integral forms ⋮ Shifted quantum affine algebras: integral forms in type \(A\) ⋮ Affine quantum Schur algebras at roots of unity ⋮ Canonical basis and Macdonald polynomials ⋮ Irreducibility criterion for a finite-dimensional highest weight representation of thesl₂loop algebra and the dimensions of reducible representations ⋮ The Kronecker quiver and bases of quantum affine \(\mathfrak{sl}_2\) ⋮ A PBW basis for lusztig’s form of untwisted affine quantum groups ⋮ Loop realizations of quantum affine algebras ⋮ The \(q\)-characters at roots of unity ⋮ Quiver varieties and finite dimensional representations of quantum affine algebras

Cites Work

• New unitary representations of loop groups
• Erratum: The arithmetic theory of loop algebras
• Quantum affine algebras
• Braid group action and quantum affine algebras
• Minimal affinizations of representations of quantum groups: The nonsimply-laced case
• Yangians, integrable quantum systems and Dorey's rule
• Quantum affine algebras and affine Hecke algebras
• Quantum Coadjoint Action
• Finite-dimensional representations of quantum affine algebras at roots of unity
• Introduction to quantum groups
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