Combinatorial Algorithms for Binary Operations on LR-tableaux with Entries Equal to 1 with Applications to Nilpotent Linear Operators

Abstract

In the paper we investigate an algorithmic associative binary operation * on the set ℒℛ1 of Littlewood-Richardson tableaux with entries equal to one. We extend * to an algorithmic nonassociative binary operation on the set ℒℛ1 × ℕ and show that it is equivalent to the operation of taking the generi c extensions of objects in the category of homomorphisms from semisimple nilpotent linear operators to nilpotent linear operators. Thus we get a combinatorial algorithm computing generic extensions in this category.