On The Unitarization Of Linear Representations Of Primitive Partially Ordered Sets

@article{Grushevoy2009OnTU,
  title={On The Unitarization Of Linear Representations Of Primitive Partially Ordered Sets},
  author={Roman Grushevoy and Kostyantyn Yusenko},
  journal={arXiv: Representation Theory},
  year={2009},
  pages={279-294}
}
We describe all weights which are appropriated for the unitarization of indecomposable linear representations of primitive partially ordered sets of finite type. 

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References

SHOWING 1-10 OF 16 REFERENCES

Locally Scalar Graph Representations in the Category of Hilbert Spaces

The condition of being locally scalar is imposed on graph (or quiver) representations in the category of Hilbert spaces. Under this condition, reflection and Coxeter functors are constructed in

THE SPECTRAL PROBLEM AND *-REPRESENTATIONS OF ALGEBRAS ASSOCIATED WITH DYNKIN GRAPHS

We study the connection between *-representations of algebras associated with graphs, locally-scalar graph representations and the problem about the spectrum of a sum of two Hermitian operators. For

Representations of Finite-Dimensional Algebras

1. Matrix Problems.- 2. Algebras, Modules and Categories.- 3. Radical, Decomposition, Aggregates.- 4. Finitely Spaced Modules.- 5. Finitely Represented Posets.- 6. Roots.- 7. Representations of

Locally-scalar representations of graphs in the category of Hilbert spaces

In this paper authors consider representations of graphs in Hilbert spaces applying a restriction of local scalarity on them. It enables to obtain a theory, similar to the classical theory of

On the complexity of description of representations of *-algebras generated by idempotents

In this paper, we introduce a quasiorder >(majorization) on *algebras with respect to the complexity of description of their representations. We show that C*(F2) >A for any finitely generated

Orthoscalar representations of quivers in the category of Hilbert spaces

AbstractAs is known, finitely presented quivers correspond to Dynkin graphs (Gabriel, 1972) and tame quivers correspond to extended Dynkin graphs (Donovan and Freislich, Nazarova, 1973). In the

Blow-up of semilinear PDE's at the critical dimension. A probabilistic approach

We present a probabilistic approach which proves blow-up of solutions of the Fujita equation ∂w/∂t = -(-Δ) α/2 w + w 1+β in the critical dimension d = α/β. By using the Feynman-Kac representation

The representation theory of finite graphs and associated algebras