The Spectral Problem and Algebras Associated with Extended Dynkin Graphs

2009/04/06 by Stanislav Popovych, Popovych, Stanislav
Mathematics · #16G20 #16W10 #47L30 #FOS: Mathematics #Functional Analysis (math.FA) #Representation Theory (math.RT) #math.FA #math.RT #msc:16G20 #msc:16W10 #msc:47L30

paper · pdf · doi:10.48550/arxiv.0904.0968

arxiv created 2009/04/06 · arxiv updated 2009/12/01

Abstract

The Spectral Problem is to describe possible spectra σ(A_j) for an irreducible n-tuple of Hermitian operators s.t. A₁+...+A_n is a scalar operator. In case when m_j= | σ(A_j)| are finite and a rooted tree \rm T_{m1,..., mn} with n branches of lengths m₁, ..., 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 (m₁, ..., m_n) ∈ \(2,2,2,2), (3,3,3), (4,4,2), (6,3,2)\ is presented.

Related

• The spectral problem and algebras associated with extended Dynkin graphs. I
• The spectral problem and *-representations of algebras associated with Dynkin graphs
• On the walk matrix of the Dynkin graph D_n
• Spectral characterization of a specific class of trees
• On *-representations of a certain class of algebras related to a graph