The boundary of the Gelfand-Tsetlin graph: A new approach

DOI10.1016/j.aim.2012.04.005zbMath1245.05131arXiv1109.1412OpenAlexW2033546838MaRDI QIDQ436124

Grigori Olshanski, Alexei Borodin

Publication date: 30 July 2012

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1109.1412

zbMATH Keywords

Schur functionsGelfand-Tsetlin graphdual Schur functionsGelfand-Tsetlin schemestotally positive sequencesunitary group characters

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Graph representations (geometric and intersection representations, etc.) (05C62)

Related Items (31)

Approximation of Markov dynamics on the dual object of the infinite-dimensional unitary group ⋮ Interpolation Macdonald polynomials and Cauchy-type identities ⋮ Convergence and an explicit formula for the joint moments of the circular Jacobi \(\beta\)-ensemble characteristic polynomial ⋮ The representation ring of the unitary groups and Markov processes of algebraic origin ⋮ Extended Gelfand-Tsetlin graph, its \(q\)-boundary, and \(q\)-B-splines ⋮ On a gateway between the Laguerre process and dynamics on partitions ⋮ Pieri integral formula and asymptotics of Jack unitary characters ⋮ Multivariate Jacobi polynomials and the Selberg integral ⋮ Multiplicative characters and Gaussian fluctuation limits ⋮ A quantization of the harmonic analysis on the infinite-dimensional unitary group ⋮ \(q\)-deformed character theory for infinite-dimensional symplectic and orthogonal groups ⋮ Integrable systems and crystals for edge labeled tableaux ⋮ Lozenge tilings of hexagons with arbitrary dents ⋮ Determinantal measures related to big \(q\)-Jacobi polynomials ⋮ Ninth variation of classical group characters of type A-D and Littlewood identities ⋮ Finite traces and representations of the group of infinite matrices over a finite field ⋮ Entropy of Schur-Weyl measures ⋮ Asymptotics of random lozenge tilings via Gelfand-Tsetlin schemes ⋮ Random surface growth and Karlin-McGregor polynomials ⋮ Universality of local statistics for noncolliding random walks ⋮ Fluctuations of particle systems determined by Schur generating functions ⋮ Determinantal structures in space-inhomogeneous dynamics on interlacing arrays ⋮ Plancherel representations of \(U(\infty)\) and correlated Gaussian free fields ⋮ Law of large numbers for infinite random matrices over a finite field ⋮ Grigori Iosifovich Olshanski ⋮ The boundary of the orbital beta process ⋮ Mapping TASEP Back in time ⋮ Markov dynamics on the dual object to the infinite-dimensional unitary group ⋮ Asymptotics of symmetric polynomials with applications to statistical mechanics and representation theory ⋮ Limit shapes for growing extreme characters of \(U(\infty)\) ⋮ Representations of classical Lie groups and quantized free convolution

Cites Work

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