Kirillov–Reshetikhin Modules of Generalized Quantum Groups of Type

  • Jae-Hoon Kwon

    Seoul National University, Republic of Korea
  • Masato Okado

    Osaka City University, Japan
Kirillov–Reshetikhin Modules of Generalized Quantum Groups of Type $A$ cover

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Abstract

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. 993–1039

DOI 10.4171/PRIMS/57-3-9