Lattice path combinatorics and asymptotics of multiplicities of weights in tensor powers

DOI10.1016/j.jfa.2004.01.004zbMath1062.22026arXivmath/0305251OpenAlexW2101356342MaRDI QIDQ705324

Tatsuya Tate, Steven Zelditch

Publication date: 26 January 2005

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0305251

zbMATH Keywords

asymptotic estimatestensor powercentral limit regionlattice path with steps in a convex polytopemultiplicity of a weightstrong deviations region

Mathematics Subject Classification ID

Analysis on real and complex Lie groups (22E30)

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Limit shape for infinite rank limit of tensor power decomposition for Lie algebras of series so2n+1 ^*, Statistics of irreducible components in large tensor powers of the spinor representation for \(\mathfrak{so}_{2n+1}\) as \(n \rightarrow \infty \), Probability measure near the boundary of tensor power decomposition for \(\mathfrak{so}_{2n+1}\), Asymptotics for the number of walks in a Weyl chamber of typeB, Asymptotics of matrix integrals and tensor invariants of compact Lie groups, Expected degree of weights in Demazure modules of \({\widehat{\mathfrak{sl}}_2}\), On the asymptotics of multiplicities for large tensor product of representations of simple Lie algebras, Towards counting paths in lattice path models with filter restrictions and long steps, Skew Howe duality and limit shapes of Young diagrams, Convergence rates of random walk on irreducible representations of finite groups, Distributions defined by \(q\)-supernomials, fusion products, and Demazure modules, Large tensor products and Littlewood-Richardson coefficients, Large deviation principle for moment map estimation, On multiplicities of irreducibles in large tensor product of representations of simple Lie algebras, The $q$-analog of Kostant's partition function and the highest root of the classical Lie algebras, Higher Dimensional Lattice Walks: Connecting Combinatorial and Analytic Behavior, Schur asymptotics of Veronese syzygies

Cites Work

• Random walks in Weyl chambers and the decomposition of tensor powers
• The theory of large deviations: from Boltzmann's 1877 calculation to equilibrium macrostates in 2D turbulence
• Projections of orbits and asymptotic behavior of multiplicities for compact connected Lie groups
• Introduction to Toric Varieties. (AM-131)
• A Large Deviation Principle for the Reduction of Product Representations
• Random Walk in a Weyl Chamber
• Random polynomials with prescribed Newton polytope
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