Log-concavity of multiplicities with application to characters of \(U(\infty)\)

DOI10.1006/aima.1997.1622zbMath0910.22011OpenAlexW2090745496WikidataQ112631896 ScholiaQ112631896MaRDI QIDQ1369693

Andrei Okounkov

Publication date: 25 November 1997

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

Full work available at URL: https://doi.org/10.1006/aima.1997.1622

zbMATH Keywords

log-concavityGelfand-Tsetlin patternscharacters of Lie groupsinfinite unitary group \(U(\infty)\)

Mathematics Subject Classification ID

Semisimple Lie groups and their representations (22E46)

Related Items (19)

Positivity among \(P\)-partition generating functions ⋮ Kazhdan-Lusztig immanants and products of matrix minors ⋮ Schur positivity and the \(q\)-log-convexity of the Narayana polynomials ⋮ Maximal supports and Schur-positivity among connected skew shapes ⋮ On a convexity property of tensor products of irreducible, rational representations of $SL(n)$ ⋮ The boundary of the Gelfand-Tsetlin graph: A new approach ⋮ Temperley-Lieb Pfaffinants and Schur \(Q\)-positivity conjectures ⋮ Coincidences among skew Schur functions ⋮ Cell transfer and monomial positivity ⋮ On products of \({\mathfrak {sl}}_{n}\) characters and support containment ⋮ Necessary conditions for Schur-maximality ⋮ Log-concavity of complexity one Hamiltonian torus actions ⋮ Log-concavity of the Duistermaat-Heckman measure for semifree Hamiltonian $S^1$-actions ⋮ Schur-positivity in a square ⋮ Necessary conditions for Schur-positivity ⋮ Positivity results on ribbon Schur function differences ⋮ Schur positivity of skew Schur function differences and applications to ribbons and Schubert classes ⋮ Schur positivity and log-concavity related to longest increasing subsequences ⋮ Newell-Littlewood numbers

Cites Work

• Coincidence probabilities
• The Capelli identity, the double commutant theorem, and multiplicity-free actions
• Binomial determinants, paths, and hook length formulae
• Projections of orbits and asymptotic behavior of multiplicities for compact connected Lie groups
• Geometric quantization and multiplicities of group representations
• Représentations factorielles de type \(II_1\) de \(U(\infty)\)
• Thoma's theorem and representations of the infinite bisymmetric group
• Logarithmic convexity of push-forward measures
• Brunn-Minkowski inequality for multiplicities
• Unimodal, log-concave and Pólya frequency sequences in combinatorics
• On the Generating Function of a Doubly Infinite, Totally Positive Sequence
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Log-concavity of multiplicities with application to characters of \(U(\infty)\)