Limit shape for infinite rank limit of tensor power decomposition for Lie algebras of series so(2n+1)

Standard

Limit shape for infinite rank limit of tensor power decomposition for Lie algebras of series so(2n+1). / Nazarov, Anton ; Nikitin, Pavel ; Postnova, Olga.

In: Journal of Physics A: Mathematical and Theoretical, Vol. 56, No. 13, 31.03.2023, p. 134001.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{2f0e1b6499c54a71b3a7e7cb4bc153ad,

title = "Limit shape for infinite rank limit of tensor power decomposition for Lie algebras of series so(2n+1)",

abstract = "We consider the Plancherel measure on irreducible components of tensor powers of the spinor representation of $\mathfrak{so}_{2n+1}$. 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.",

keywords = "Berele insertion, Lie algebras, Young diagram, central limit theorem, determinantal point process, limit shapes, special orthogonal group",

author = "Anton Nazarov and Pavel Nikitin and Olga Postnova",

year = "2023",

month = mar,

day = "31",

doi = "10.1088/1751-8121/acbd73",

language = "English",

volume = "56",

pages = "134001",

journal = "Journal of Physics A: Mathematical and Theoretical",

issn = "1751-8113",

publisher = "IOP Publishing Ltd.",

number = "13",

}

RIS

TY - JOUR

T1 - Limit shape for infinite rank limit of tensor power decomposition for Lie algebras of series so(2n+1)

AU - Nazarov, Anton

AU - Nikitin, Pavel

AU - Postnova, Olga

PY - 2023/3/31

Y1 - 2023/3/31

N2 - We consider the Plancherel measure on irreducible components of tensor powers of the spinor representation of $\mathfrak{so}_{2n+1}$. 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.

AB - We consider the Plancherel measure on irreducible components of tensor powers of the spinor representation of $\mathfrak{so}_{2n+1}$. 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.

KW - Berele insertion

KW - Lie algebras

KW - Young diagram

KW - central limit theorem

KW - determinantal point process

KW - limit shapes

KW - special orthogonal group

UR - https://www.mendeley.com/catalogue/4eb84af0-41f4-3067-aab2-8ede5cc78140/

U2 - 10.1088/1751-8121/acbd73

DO - 10.1088/1751-8121/acbd73

M3 - Article

VL - 56

SP - 134001

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 13

ER -

ID: 104597567