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arXiv · 0904.0968

The Spectral Problem and Algebras Associated with Extended Dynkin Graphs

Stanislav Popovych
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Abstract

The Spectral Problem is to describe possible spectra $σ(A_j)$ for an irreducible $n$-tuple of Hermitian operators s.t. $A_1+...+A_n$ is a scalar operator. In case when $m_j= | σ(A_j)|$ are finite and a rooted tree ${\rm T}_{m_1,..., m_n}$ with $n$ branches of lengths $m_1, ..., m_n$ is a Dynkin graph the explicit answer to the Spectral Problem was given recently by S. A. Kruglyak, S. V. Popovych, and Yu. S. Samo\vılenko. In present work the solution of the Spectral Problem for all star-shaped simply laced extended Dynkin graphs, i.e. when $(m_1, ..., m_n) \in \{(2,2,2,2), (3,3,3), (4,4,2)$, $(6,3,2)\}$ is presented.

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Stanislav Popovych. 2009-04-06. The Spectral Problem and Algebras Associated with Extended Dynkin Graphs. https://arxiv.org/abs/0904.0968

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