arXiv subjects

Karolina Vocke

Publications and source records attributed to Karolina Vocke.

3 recordsLinked to original sources

arXiv2026

Many-to-many stable matching in large economies

We study stability notions for networked many-to-many matching markets with individually insignificant agents in distributional form. Outcomes are formulated as joint distributions over characteristics of agents and contract choices. Characteristics can lie in an arbitrary Polish space. We provide a mechanical method for transferring existence results for finite matching models to large matching models for many stability notions. In particular, we show that tree-stable and pairwise-stable outcomes exist.

econ.TH↗

arXiv2024

On Borel subalgebras of quantum groups

For a quantum group, we study those right coideal subalgebras, for which all irreducible representations are one-dimensional. If a right coideal subalgebra is maximal with this property, then we call it a Borel subalgebra. Besides the positive part of the quantum group and its reflections, we find new unfamiliar Borel subalgebras, for example, ones containing copies of the quantum Weyl algebra. Given a Borel subalgebra, we study its induced (Verma-)modules and prove among others that they have all irreducible finite-dimensional modules as quotients. We give two structural conjectures involving the associated graded right coideal subalgebra, which we prove in certain cases. In particular, they predict the shape of all triangular Borel subalgebras. As examples, we determine all Borel subalgebras of $U_q(\mathfrak{sl}_2)$ and $U_q(\mathfrak{sl}_3)$ and discuss the induced modules.

math.QA↗

arXiv2018

On right coideal subalgebras of quantum groups

Right coideal subalgebras are interesting substructures of Hopf algebras such as quantum groups. Examples of right coideal subalgebras are the quantum Borel part as well as quantum symmetric pairs. Classifying right coideal subalgebras is a difficult question with notable results by Schneider, Heckenberger and Kolb. After reviewing these results, as main result we prove that an arbitrary right coideal subalgebras has a particularly nice set of generators. This allows in principle to specify the set of right coideal subalgebras in a given case. As application we determine right coideal subalgebras of the quantum groups Uq(sl2) and Uq(sl3) and discuss their representation theoretic properties.

math.QA↗