2020/11/21 by Gopal Goel, Andrew Chi-Chih Yao, Goel, Gopal +1
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications #Representation Theory (math.RT) #Spectral Theory (math.SP)
paper · pdf · doi:10.48550/arxiv.2011.10724
openalex publication_date 2020/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a family of measures originating from the signatures of the irreducible components of representations of the unitary group, as the size of the group goes to infinity. Given a random signature λ of length N with counting measure m, we obtain a random signature μ of length N-1 through projection onto a unitary group of lower dimension. The signature μ interlaces with the signature λ, and we record the data of μ,λ in a random rectangular Young diagram w. We show that under a certain set of conditions on λ, both m and w converge as N→∞. We provide an explicit moment generating function relationship between the limiting objects. We further show that the moment generating function relationship induces a bijection between bounded measures and certain continual Young diagrams, which can be viewed as a quantized analogue of the Markov-Krein correspondence.