Kleiner's theorem for unitary representations of posets

Autor(es)

Samoilenko, Yurii ^[1] ; Yusenko, Kostyantyn ^[2]

Afiliação do(s) autor(es)

^[1] Ukrainian Acad Sci, Inst Math, Kiev - Ukraine

^[2] Univ Sao Paulo, Dept Math, BR-05508 Sao Paulo - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Linear Algebra and its Applications; v. 437, n. 2, p. 581-588, JUL 15 2012.
• Citações Web of Science: 6

Resumo

A subspace representation of a poset S = [s(1), ..., S-t] is given by a system (V; V-1, ..., V-t) consisting of a vector space V and its sub-spaces V-i such that V-i subset of V-j if s(i) (sic) S-j. For each real-valued vector chi = (chi(1), ..., chi(t)) with positive components, we define a unitary chi-representation of S as a system (U: U-1, ..., U-t) that consists of a unitary space U and its subspaces U-i such that U-i subset of U-j if S-i (sic) S-j and satisfies chi 1 P-1 + ... + chi P-t(t) = 1, in which P-i is the orthogonal projection onto U-i. We prove that S has a finite number of unitarily nonequivalent indecomposable chi-representations for each weight chi if and only if S has a finite number of nonequivalent indecomposable subspace representations; that is, if and only if S contains any of Kleiner's critical posets. (c) 2012 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 10/15781-0 - Feixes vetoriais estáveis sobre plano projetivo e representações de posets em categoria de espaços unitários
• Beneficiário: Kostiantyn Iusenko
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado