Uniform description of the rigged configuration bijection

An Explicit Algorithm of Rigged Configuration Bijection for the Adjoint Crystal of Type $G_{2}^{(1)}$

“…i − 1, and p (a) i − 2, respectively. Here, "q-singular" is the abbreviation of "quasi singular" firstly introduced in [19] and commonly used in the literature [29,35]. The "qqsingular" strings are firstly introduced in this paper.…”

“…The bijection of Kerov, Kirillov, and Reshetikhin is a bijection from rigged configurations to the paths of the form (B 1,1 ) ⊗L in type A (1) n where B r,s denotes the KR crystal. Until now, this has been extended in more general setting and in various types [3,14,25,26,27,28,23,24,30,31,34,35,32]. For nonexceptional types, the generalization of the rigged configuration bijection has been established [29].…”

“…This paper concerns one of these problems. For the G (1) 2 adjoint crystals, the explicit algorithm of the rigged configuration bijection Φ is not known as pointed out in [35] though the crystal structure is very simple (see Fig. 2.2).…”