Kirillov–Reshetikhin Modules of Generalized Quantum Groups of Type
Jae-Hoon KwonSeoul National University, Republic of Korea
Masato OkadoOsaka City University, Japan
The generalized quantum group of type is an affine analogue of the quantum group associated to a general linear Lie superalgebra, which appears in the study of solutions to the tetrahedron equation or the three-dimensional Yang–Baxter equation. In this paper we develop the crystal base theory for finite-dimensional representations of generalized quantum groups of type . As the main result, we construct Kirillov–Reshetikhin modules, that is, a family of irreducible modules which have crystal bases. We also give an explicit combinatorial description of the crystal structure of Kirillov–Reshetikhin modules, the combinatorial matrix and the energy function on their tensor products.
Cite this article
Jae-Hoon Kwon, Masato Okado, Kirillov–Reshetikhin Modules of Generalized Quantum Groups of Type . Publ. Res. Inst. Math. Sci. 57 (2021), no. 3/4, pp. 993–1039DOI 10.4171/PRIMS/57-3-9