Graded Specht Modules as Bernstein–Zelevinsky Derivatives of the RSK Model

Abstract We clarify the links between graded Specht construction of modules over cyclotomic Hecke algebras and Robinson-Schensted-Knuth (RSK) for quiver type $A$, which was recently imported from setting representations $p$-adic groups. For that goal we develop a theory crystal derivative operators on algebra categorifies Berenstein–Zelevinsky strings framework quantum groups generalizes variant classical Bernstein–Zelevinsky derivatives setting. Graded decomposition numbers are shown to be special subfamily wider concept RSK numbers.