The Hopf algebra \(\text{Rep\,} U_q \widehat{\mathfrak g\mathfrak l}_\infty\)

zbMath1034.17009arXivmath/0103126MaRDI QIDQ1871758

Evgenii E. Mukhin, Edward V. Frenkel'

Publication date: 4 May 2003

Published in: Selecta Mathematica. New Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0103126

zbMATH Keywords

Hopf algebraGrothendieck groupHall algebrapolynomial representationaffine Hecke algebra\(q\)-character homomorphismquantum affine groupquantum Frobenius homomorphism

Mathematics Subject Classification ID

Related Items (32)

A note on odd reflections of super Yangian and Bethe ansatz ⋮ Small representations for affine \(q\)-Schur algebras ⋮ Uhlenbeck spaces for \(\mathbb{A}^2\) and affine Lie algebra \(\widehat {\mathfrak {sl}}_n\) ⋮ Higher Sugawara operators for the quantum affine algebras of type \(A\) ⋮ Identification of simple representations for affine \(q\)-Schur algebras ⋮ Standard multipartitions and a combinatorial affine Schur-Weyl duality ⋮ Finite type modules and Bethe ansatz equations ⋮ Asymptotic representations of quantum affine superalgebras ⋮ Quantum geometry and quiver gauge theories ⋮ Length-two representations of quantum affine superalgebras and Baxter operators ⋮ Yangian Characters and Classical $$\mathcal{W}$$ -Algebras ⋮ Isomorphism between the \(R\)-matrix and Drinfeld presentations of quantum affine algebra: types \(B\) and \(D\) ⋮ A note on \(q\)-oscillator realizations of \(U_q(gl(M|N))\) for Baxter \(Q\)-operators ⋮ Representations of quantum affine algebras of type $B_N$ ⋮ \(R\)-matrix presentation of quantum affine algebra in type \(A_{2n-1}^{(2)}\) ⋮ Blocks of affine quantum Schur algebras ⋮ Quantum loop algebras and \(\ell\)-root operators ⋮ Isomorphism between the R-matrix and Drinfeld presentations of quantum affine algebra: Type C ⋮ Extended T-systems ⋮ Quantum symmetric Kac-Moody pairs ⋮ The alternating presentation of \(U_q(\widehat{gl_2})\) from Freidel-Maillet algebras ⋮ On minimal affinizations of representations of quantum groups ⋮ Hall algebras of cyclic quivers and \(q\)-deformed Fock spaces ⋮ The algebra \(U_q(\widehat{sl}_\infty)\) and applications ⋮ Representations of twisted \(q\)-Yangians ⋮ Extremal loop weight modules for \(\mathcal {U}_q(\widehat{sl}_{\infty})\) ⋮ Quantum affine \(\mathfrak{gl}_n\) via Hecke algebras ⋮ Affine quantum Schur algebras at roots of unity ⋮ Gelfand-Tsetlin bases of representations for super Yangian and quantum affine superalgebra ⋮ On the second realization for the positive part of \(U_q (\widehat{sl_2})\) of equitable type ⋮ Freidel-Maillet type presentations of \(U_q(sl_2)\) ⋮ Generalized Demazure modules and prime representations in type \(D_n\)

This page was built for publication: The Hopf algebra \(\text{Rep\,} U_q \widehat{\mathfrak g\mathfrak l}_\infty\)