For a Hilbert space $H$, we study configurations of its subspaces related to Coxeter graphs $\mathbb{G}_{s_1,s_2}$, $s_1,s_2\in\{4,5\}$, which are arbitrary trees such that one edge has type~$s_1$, another one has type~$s_2$ and the rest are of type~$3$. We prove that such irreducible configurations exist only in a finite dimensional $H$, where the dimension of $H$ does not exceed the number of vertices of the graph by more than twice. We give a description of all irreducible nonequivalent configurations; they are indexed with a continuous parameter. As an example, we study irreducible configurations related to a graph that consists of three vertices and two edges of type $s_1$ and $s_2$.

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Title

On *-representations of a class of algebras with polynomial growth related to Coxeter graphs

N. D. Popova and A. V. Strelets, On *-representations of a class of algebras with polynomial growth related to Coxeter graphs, Methods Funct. Anal. Topology 17
(2011), no. 3, 252-273.

BibTex

@article {MFAT595,
AUTHOR = {Popova, N. D. and Strelets, A. V.},
TITLE = {On *-representations of a class of algebras with polynomial growth related to Coxeter graphs},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {17},
YEAR = {2011},
NUMBER = {3},
PAGES = {252-273},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=595},
}