Limit shape for infinite rank limit of tensor power decomposition for Lie algebras of series so2n+1. (31st March 2023)

• Record Type: Journal Article
• Authors: Nazarov, Anton; Nikitin, Pavel; Postnova, Olga
• Is Part Of: Journal of physics. Volume 56:Number 13(2023)
• Publication Date: 2023-03-31
• Subjects: limit shapes -- Lie algebras -- special orthogonal group -- central limit theorem -- determinantal point process -- Young diagram -- Berele insertion; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/acbd73
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: We consider the Plancherel measure on irreducible components of tensor powers of the spinor representation of s o 2 n + 1 . The irreducible representations correspond to the generalized Young diagrams. With respect to this measure the probability of an irreducible representation is the product of its multiplicity and dimension, divided by the total dimension of the tensor product. We study the limit shape of the generalized Young diagram when the tensor power N and the rank n of the algebra tend to infinity with N / n fixed. We derive an explicit formula for the limit shape and prove convergence to it in probability. We prove central limit theorem for global fluctuations around the limit shape.