# 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}
}
• Published 1 July 2008
• Mathematics
• arXiv: Representation Theory
We describe all weights which are appropriated for the unitarization of indecomposable linear representations of primitive partially ordered sets of finite type.
4 Citations

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## References

SHOWING 1-10 OF 16 REFERENCES

### Locally Scalar Graph Representations in the Category of Hilbert Spaces

• Mathematics
• 2005
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

• Mathematics
• 2004
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

• Mathematics
• 1992
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

• Mathematics
• 2003
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

• Mathematics
• 2000
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

• Mathematics
• 2007
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

• Mathematics
• 2002
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