2019/07/17 by Lauren C. Ruth, Ruth, Lauren C.
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Analytic Number Theory Research #Art #Backslash #Combinatorics #Discrete mathematics #FOS: Mathematics #Humanities #Lambda #Lattice (music) #Mathematical analysis #Mathematics #Multiplicity (mathematics) #Operator Algebras (math.OA) #Physics #Pointwise #Pointwise convergence #Representation Theory (math.RT) #Subspace topology #advanced mathematical theories #math.OA #math.RT
paper · pdf · open access · doi:10.48550/arxiv.1907.07641
published in arXiv (Cornell University) (Cornell University) · 5 pages
arxiv created 2019/07/17 · openalex publication_date 2019/07/17 · arxiv updated 2019/07/18 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
Let G be PGL(n,F), n ≥ 3, F a certain non-archimedean local field; or let G be PSL(2,ℝ) × ⋯ × PSL(2,ℝ). Let Γ be a lattice in G, and let ( Λn ) be a sequence of lattices in G satisfying the pointwise limit multiplicity property. In this note, we explain how the pointwise limit multiplicity property can be combined with a generalization of a theorem in \citeghj to give representations of the II1 factor R Γ on a subspace of L2(Λi \backslash G) for some Λi in ( Λn ). This extends a result in the author's dissertation \citeruthphd.