Polyhedral realizations of crystal bases \(B(\lambda)\) for quantum algebras of nonexceptional affine types. (English) Zbl 1428.82063
Summary: We give explicit forms of the crystal bases \(B(\lambda)\) for the integrable highest weight modules of the quantum affine algebras for \(A_{2 n}^{(2)}, A_{2 n - 1}^{(2)}, B_n^{(1)}, C_n^{(1)}\), and \(D_{n + 1}^{(2)}\).
©2019 American Institute of Physics
©2019 American Institute of Physics
MSC:
| 82D25 | Statistical mechanics of crystals |
| 52B20 | Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) |
| 81R50 | Quantum groups and related algebraic methods applied to problems in quantum theory |
| 17B37 | Quantum groups (quantized enveloping algebras) and related deformations |
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