Two-Parameter Quantum Groups and -Matrices: Classical Types
We construct finite -matrices for the first fundamental representation of two-parameter quantum groups ᵣ,ₛ() for classical , both through the decomposition of ⊗ into irreducibles ᵣ,ₛ()-submodules as well as by evaluating the universal R-matrix. The latter is crucially based on the construction of...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2025 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2025
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/214100 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Two-Parameter Quantum Groups and -Matrices: Classical Types. Ian Martin and Alexander Tsymbaliuk. SIGMA 21 (2025), 064, 54 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | We construct finite -matrices for the first fundamental representation of two-parameter quantum groups ᵣ,ₛ() for classical , both through the decomposition of ⊗ into irreducibles ᵣ,ₛ()-submodules as well as by evaluating the universal R-matrix. The latter is crucially based on the construction of dual PBW-type bases of ⁺⁻ᵣ,ₛ() consisting of the ordered products of quantum root vectors defined via (, )-bracketings and combinatorics of standard Lyndon words. We further derive explicit formulas for affine -matrices, both through the Yang-Baxterization technique of [Internat. J. Modern Phys. A 6 (1991), 3735-3779] and as the unique intertwiner between the tensor product of (u) and (v), viewed as modules over two-parameter quantum affine algebras ᵣ,ₛ(ˆ) for classical . The latter generalizes the formulas of [Comm. Math. Phys. 102 (1986), 537-547] for one-parametric quantum affine algebras.
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| ISSN: | 1815-0659 |