Young wall models for the level 1 highest weight and Fock space crystals of \(U_q (E_6^{(2)})\) and \(U_q (F_4^{(1)})\). (English) Zbl 07930037
Summary: In this paper, we construct Young wall models for the level 1 highest weight and Fock space crystals of quantum affine algebras in types \(E_6^{(2)}\) and \(F_4^{(1)}\). Our starting point in each case is a combinatorial realization for a certain level 1 perfect crystal in terms of Young columns. Then, using energy functions and affine energy functions we define the notions of reduced and proper Young walls, which model the highest weight and Fock space crystals, respectively.
MSC:
| 05E10 | Combinatorial aspects of representation theory |
| 17B37 | Quantum groups (quantized enveloping algebras) and related deformations |
| 20G42 | Quantum groups (quantized function algebras) and their representations |
Keywords:
exceptional quantum affine algebra; perfect crystal; energy function; Young column; Young wall; Fock spaceReferences:
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