Almost invariant subspaces and operators

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

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

标准 Young 表上的两种偏序及其在幂零线性算子不变子空间中的应用

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

该研究考察标准 Young 表上的两种偏序，并阐明其在幂零线性算子不变子空间理论中的应用。

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

We study geometric properties of varieties associated with invariant subspaces of nilpotent operators. There are reductive algebraic groups acting on these varieties. We give dimensions of orbits of these actions. Moreover, a combinatorial characterization of the partial order given by degenerations is described.

Classification of the invariant subspaces of the Lawrence-Krammer representation

The Lawrence-Krammer representation was used in $2000$ to show the linearity of the braid group. The problem had remained open for many years. The fact that the Lawrence-Krammer representation of the braid group is reducible for some complex values of its two parameters is now known, as well as the complete description of these values under some restrictions on one of the parameters. It is also known that when the representation is reducible, the action on a proper invariant subspace is an Iwahori-Hecke algebra action. In this paper, we prove a theorem of classification for the invariant subsp…

Invariant Krein subspaces, regular irreducibility and integral representations

We study unitary representations of groups in Krein spaces, irreducibility criteria and integral decompositions. Our main tool is the theory of Krein subspaces and their (reproducing) kernels and a variant of Choquet's theorem.

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

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 invariant subspaces of nilpotent linear operators. Moreover, we discuss geometric properties of generic extensions and their connections with combinatorics.