View in EDS

Limit shape for infinite rank limit of tensor power decomposition for Lie algebras of series so2n+1.

Saved in:
Bibliographic Details
Title: Limit shape for infinite rank limit of tensor power decomposition for Lie algebras of series so2n+1.
Authors: Nazarov, Anton1 (AUTHOR) antonnaz@gmail.com, Nikitin, Pavel2,3 (AUTHOR), Postnova, Olga4 (AUTHOR)
Source: Journal of Physics A: Mathematical & Theoretical. 3/31/2023, Vol. 56 Issue 13, p1-33. 33p.
Subjects: Lie algebras, Central limit theorem, Probability measures, Tensor products, Algebra
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. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Physics A: Mathematical & Theoretical is the property of IOP Publishing and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
Description
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. [ABSTRACT FROM AUTHOR]
ISSN:17518113
DOI:10.1088/1751-8121/acbd73