Systematic method to traverse generation at fixed Young tableau

Develop a systematic procedure to move between generations while keeping the SO(25) Young tableau (i.e., the Lorentz representation shape) of the state fixed in the open bosonic string spectrum, within the authors’ light-cone framework.

Background

The paper introduces the notion of generation as the number of times a given Young tableau has appeared at lower levels and shows how to construct trajectories at fixed generation. However, while trajectories can be climbed by adding oscillators, relating states across generations for a fixed tableau remains challenging in the light-cone approach.

An explicit, systematic method to raise generation without changing the Lorentz representation would greatly expand constructive control over the spectrum.