# Crystal bases of modified quantized enveloping algebras and a double RSK correspondence - Mathematics > Representation Theory

Abstract: The crystal base of the modified quantized enveloping algebras of type$A {+\infty}$ or $A \infty$ is realized as a set of integral bimatrices. It isobtained by describing the decomposition of the tensor product of a highestweight crystal and a lowest weight crystal into extremal weight crystals, andtaking its limit using a tableaux model of extremal weight crystals. Thisrealization induces in a purely combinatorial way a bicrystal structure of thecrystal base of the modified quantized enveloping algebras and hence itsPeter-Weyl type decomposition generalizing the classical RSK correspondence.

Author: Jae-Hoon Kwon

Source: https://arxiv.org/