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

Article type: Research Article

Authors: Kaniecki, Mariusz^{; *} | Kosakowska, Justyna

Affiliations: Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Poland. kanies@mat.umk.pl, justus@mat.umk.pl

Correspondence: [*] Address for correspondence: Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Poland.

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 generic 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.

Keywords: Littlewood-Richardson tableaux, partitions, invariant subspaces, nilpotent linear operators, generic extensions, pickets, degeneration partial order, combinatorial algorithms

DOI: 10.3233/FI-2020-1935

Journal: Fundamenta Informaticae, vol. 174, no. 2, pp. 121-136, 2020