Variation über ein Thema von Knuth, Robinson, Schensted und Schützenberger

Abstract

The crucial point of many approaches to representation theory of symmetric groups is the algorithm of Robinson and Schensted. Roughly speaking, this is a sorting algorithm with documentation. Prom the theorem of Schützenberger we take the idea for a description of the Robinson-Schensted correspondence without using the documentation part of the algorithm, which therefore plays no role in our approach. On the other hand we analyze the Knuth relations more thoroughly than usual. By means of a slight generalization of the sorting part of the algorithm we get another associative product on the free monoid X* over a countable alphabet X. The canonical map of X* onto the plactic monoid is also a homomorphism with respect to this product.

Dieser Artikel entstand im Rahmen des DFG-Projekts BL 488/1-1.