Kirillov--Reshetikhin Modules of Generalized Quantum Groups of Type A.

The generalized quantum group of type A 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 A. 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 R matrix and the energy function on their tensor products. [ABSTRACT FROM AUTHOR]