J. Kosakowska

activity

20092023

most citedLie algebras associated with quadratic forms and their applications to Ringel-Hall algebras

17 citations · 59 across the 16 of their papers we have counts for

collaborators

17 papers

math.GR2023

Abelian p-groups with a fixed elementary subgroup or with a fixed elementary quotient

Justyna Kosakowska, Markus Schmidmeier, Martin Schreiner

In his 1934 paper, G.\ Birkhoff poses the problem of classifying pairs $(G, U)$ where $G$ is an abelian group and $U \subset G$ a subgroup, up to automorphisms of $G$ . In general, Bi…

math.RT2023

Two partial orders on Standard Young Tableaux with applications to invariant subspaces of nilpotent linear operators

Mariusz Kaniecki, Justyna Kosakowska

In the paper we investigate two partial orders on standard Young tableaux and show their applications in the theory of invariant subspaces of nilpotent linear operators.

math.RT2020

The existence of Hall polynomials for $x^{2}$ -bounded invariant subspaces of nilpotent linear operators

Stanisław Kasjan, Justyna Kosakowska

We prove the existence of Hall polynomials for $x^{2}$ -bounded invariant subspaces of nilpotent linear operators.

math.RT2020★ 1 cited

The socle tableau as a dual version of the Littlewood-Richardson tableau

Justyna Kosakowska, Markus Schmidmeier

Like the LR-tableau, a socle tableau is given as a skew diagram with certain entries. Unlike in the LR-tableau, the entries in the socle tableau are weakly increasing in each row,…

math.RT2020

Combinatorial algorithms for binary operations on LR-tableaux with entries equal to 1 with applications to nilpotent linear operators

Mariusz Kaniecki, Justyna Kosakowska

In the paper we investigate an algorithmic associative binary operation $*$ on the set $L R_{1}$ of Littlewood-Richardson tableaux with entries equal to one. We extend $*$ t…

math.RT2019

Finite direct sums of cyclic embeddings

Justyna Kosakowska, Markus Schmidmeier

In this paper we generalize Kaplansky's combinatorial characterization of the isomorphism types of embeddings of a cyclic subgroup in a finite abelian group given in his 1951 book…

math.RT2018

Applications of Littlewood-Richardson tableaux to computing generic extension of semisimple invariant subspaces of nilpotent linear operators

Mariusz Kaniecki, Justyna Kosakowska

The main aim of the paper is to present a~combinatorial algorithm that, applying Littlewood-Richardson tableaux with entries equal to $1$ , computes generic extensions of semisimple…

math.RT2016★ 5 cited

Operations on Arc Diagrams and Degenerations for Invariant Subspaces of Linear Operators. Part II

Mariusz Kaniecki, Justyna Kosakowska, Markus Schmidmeier

For a partition $β$ , denote by $N_{β}$ the nilpotent linear operator of Jordan type $β$ . Given partitions $β$ , $γ$ , we investigate the representation space $_{2} V_{γ}^{β}$ of a…

math.RT2016★ 6 cited

Box moves on Littlewood-Richardson tableaux and an application to invariant subspace varieties

Justyna Kosakowska, Markus Schmidmeier

In his 1951 book "Infinite Abelian Groups", Kaplansky gives a combinatorial characterization of the isomorphism types of embeddings of a cyclic subgroup in a finite abelian group.…

math.RT2015★ 1 cited

Two Partial Orders for Standard Young Tableaux

Justyna Kosakowska, Markus Schmidmeier, Hugh Thomas

In this manuscript we show that two partial orders defined on the set of standard Young tableaux of shape $α$ are equivalent. In fact, we give two proofs for the equivalence of the…

math.RT2014★ 9 cited

The boundary of the irreducible components for invariant subspace varieties

Justyna Kosakowska, Markus Schmidmeier

Given partitions $α$ , $β$ , $γ$ , the short exact sequences $0 \to N_{α} \to N_{β} \to N_{γ} \to 0$ of nilpotent linear operators of Jordan types $α$ , $β$ , $γ$ , respectively, define a construc…

math.RT2013

The existence of Hall polynomials for posets of finite prinjective type

Justyna Kosakowska

We prove the existence of Hall polynomials for prinjective representations of finite partially ordered sets of finite prinjective type. In Section 4 we shortly discuss consequences…

math.RT2013★ 17 cited

Lie algebras associated with quadratic forms and their applications to Ringel-Hall algebras

Justyna Kosakowska

We define and investigate nilpotent Lie algebras associated with quadratic forms. We also present their connections with Lie algebras and Ringel-Hall algebras associated with repre…

math.RT2012★ 4 cited

Arc diagram varieties

Justyna Kosakowska, Markus Schmidmeier

Let $k$ be an algebraically closed field and $α$ , $β$ , $γ$ be partitions. An algebraic group acts on the constructible set of short exact sequences of nilpotent $k$ -linear operator…

math.RT2012★ 16 cited

Operations on Arc Diagrams and Degenerations for Invariant Subspaces of Linear Operators

Justyna Kosakowska, Markus Schmidmeier

We study geometric properties of varieties associated with invariant subspaces of nilpotent operators. There are reductive algebraic groups acting on these varieties. We give dimen…

math.RT2011

Generic extensions of nilpotent $k [T]$ -modules, monoids of partitions and constant terms of Hall polynomials

Justyna Kosakowska

We prove that the monoid of generic extensions of finite dimensional nilpotent $k [T]$ -modules is isomorphic to the monoid of partitions (with addition of partitions). Moreover we g…

math.RT2009

On Lie algebras associated with representation directed algebras

Stanisław Kasjan, Justyna Kosakowska

Let $B$ be a representation-finite $C$ -algebra. The $Z$ -Lie algebra $L (B)$ associated with $B$ has been defined by Ch. Riedtmann. If $B$ is representation-directe…

Abelian p-groups with a fixed elementary subgroup or with a fixed elementary quotient

Two partial orders on Standard Young Tableaux with applications to invariant subspaces of nilpotent linear operators

The existence of Hall polynomials for x2-bounded invariant subspaces of nilpotent linear operators

The socle tableau as a dual version of the Littlewood-Richardson tableau

Combinatorial algorithms for binary operations on LR-tableaux with entries equal to 1 with applications to nilpotent linear operators

Finite direct sums of cyclic embeddings

Applications of Littlewood-Richardson tableaux to computing generic extension of semisimple invariant subspaces of nilpotent linear operators

Operations on Arc Diagrams and Degenerations for Invariant Subspaces of Linear Operators. Part II

Box moves on Littlewood-Richardson tableaux and an application to invariant subspace varieties

Two Partial Orders for Standard Young Tableaux

The boundary of the irreducible components for invariant subspace varieties

The existence of Hall polynomials for posets of finite prinjective type

Lie algebras associated with quadratic forms and their applications to Ringel-Hall algebras

Arc diagram varieties

Operations on Arc Diagrams and Degenerations for Invariant Subspaces of Linear Operators

Generic extensions of nilpotent k[T]-modules, monoids of partitions and constant terms of Hall polynomials

On Lie algebras associated with representation directed algebras

The existence of Hall polynomials for $x^{2}$ -bounded invariant subspaces of nilpotent linear operators

Generic extensions of nilpotent $k [T]$ -modules, monoids of partitions and constant terms of Hall polynomials