Two-parameter Quantum Groups of Exceptional Type E-Series and Convex PBW-type Basis

DOI10.1142/S100538670800059XzbMath1162.17012arXivmath/0605179MaRDI QIDQ3597571

Xiaotang Bai, Hu, Naihong

Publication date: 9 February 2009

Published in: Algebra Colloquium (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0605179

zbMATH Keywords

Drinfeld doubleuniversal \(R\)-matrixLyndon wordtwo-parameter quantum group

Mathematics Subject Classification ID

Related Items (15)

Two-parameter quantum affine algebra of type \(C_n^{(1)}\), Drinfeld realization and vertex representation ⋮ Extremal projectors of two-parameter Kashiwara algebras ⋮ Quantum subgroups of \(\text{GL}_{\alpha ,\beta }(n)\) ⋮ Quantum supergroup Ur,s(osp(1,2)), Scasimir operators and Dickson polynomials ⋮ Convex PBW-type Lyndon bases and restricted two-parameter quantum group of type \(F_4\) ⋮ Factorization of simple modules for certain restricted two-parameter quantum groups ⋮ On the centre of two-parameter quantum groups \(U_{r, s}(\mathfrak{g})\) for type \(B_n\) with \(n\) even ⋮ Notes on 2-parameter quantum groups. I. ⋮ Derivations and automorphisms of the positive part of the two-parameter quantum group \(U_{r,s}(B_{3})\) ⋮ Convex PBW-type Lyndon bases and restricted two-parameter quantum groups of type \(B\) ⋮ Two-parameter quantum vertex representations via finite groups and the McKay correspondence ⋮ On finite-dimensional representations of two-parameter quantum affine algebras ⋮ Fermionic realization of two-parameter quantum affine algebra \(U_{r,s}(\widehat{\mathfrak{sl}}_n)\) ⋮ Two-parameter quantum affine algebra of type G2(1), Drinfeld realization and vertex representation ⋮ Two-parameter Quantum Affine Algebra $U_{r,s}(\widehat{\frak{sl}}_2)$

Cites Work

• A two-parameter quantization of GL(n)
• An analogue of P.B.W. theorem and the universal R-matrix for \(U_ h\mathfrak{sl}(N+1)\)
• The two-parameter quantum group of exceptional type \(G_2\) and Lusztig's symmetries
• Two-parameter quantum groups and Drinfel'd doubles.
• Drinfel'd doubles and Lusztig's symmetries of two-parameter quantum groups
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