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The Limit Shape of a Probability Measure on a Tensor Product of Modules of the Bn Algebra. / Nazarov, A. A.; Postnova, O. V.

In: Journal of Mathematical Sciences (United States), Vol. 240, No. 5, 07.08.2019, p. 556-566.

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

Harvard

Nazarov, AA & Postnova, OV 2019, 'The Limit Shape of a Probability Measure on a Tensor Product of Modules of the Bn Algebra', Journal of Mathematical Sciences (United States), vol. 240, no. 5, pp. 556-566. https://doi.org/10.1007/s10958-019-04374-y

APA

Nazarov, A. A., & Postnova, O. V. (2019). The Limit Shape of a Probability Measure on a Tensor Product of Modules of the Bn Algebra. Journal of Mathematical Sciences (United States), 240(5), 556-566. https://doi.org/10.1007/s10958-019-04374-y

Vancouver

Nazarov AA, Postnova OV. The Limit Shape of a Probability Measure on a Tensor Product of Modules of the Bn Algebra. Journal of Mathematical Sciences (United States). 2019 Aug 7;240(5):556-566. https://doi.org/10.1007/s10958-019-04374-y

Author

Nazarov, A. A. ; Postnova, O. V. / The Limit Shape of a Probability Measure on a Tensor Product of Modules of the Bn Algebra. In: Journal of Mathematical Sciences (United States). 2019 ; Vol. 240, No. 5. pp. 556-566.

BibTeX

@article{614206e232954be7a41f9ddd957c68f9,
title = "The Limit Shape of a Probability Measure on a Tensor Product of Modules of the Bn Algebra",
abstract = "We study a probability measure on the integral dominant weights in the decomposition of the Nth tensor power of the spinor representation of the Lie algebra so(2n + 1). The probability of a dominant weight λ is defined as the dimension of the irreducible component of λ divided by the total dimension 2nN of the tensor power. We prove that as N →∞, the measure weakly converges to the radial part of the SO(2n+1)-invariant measure on so(2n+1) induced by the Killing form. Thus, we generalize Kerov{\textquoteright}s theorem for su(n) to so(2n + 1).",
author = "Nazarov, {A. A.} and Postnova, {O. V.}",
year = "2019",
month = aug,
day = "7",
doi = "10.1007/s10958-019-04374-y",
language = "English",
volume = "240",
pages = "556--566",
journal = "Journal of Mathematical Sciences",
issn = "1072-3374",
publisher = "Springer Nature",
number = "5",

}

RIS

TY - JOUR

T1 - The Limit Shape of a Probability Measure on a Tensor Product of Modules of the Bn Algebra

AU - Nazarov, A. A.

AU - Postnova, O. V.

PY - 2019/8/7

Y1 - 2019/8/7

N2 - We study a probability measure on the integral dominant weights in the decomposition of the Nth tensor power of the spinor representation of the Lie algebra so(2n + 1). The probability of a dominant weight λ is defined as the dimension of the irreducible component of λ divided by the total dimension 2nN of the tensor power. We prove that as N →∞, the measure weakly converges to the radial part of the SO(2n+1)-invariant measure on so(2n+1) induced by the Killing form. Thus, we generalize Kerov’s theorem for su(n) to so(2n + 1).

AB - We study a probability measure on the integral dominant weights in the decomposition of the Nth tensor power of the spinor representation of the Lie algebra so(2n + 1). The probability of a dominant weight λ is defined as the dimension of the irreducible component of λ divided by the total dimension 2nN of the tensor power. We prove that as N →∞, the measure weakly converges to the radial part of the SO(2n+1)-invariant measure on so(2n+1) induced by the Killing form. Thus, we generalize Kerov’s theorem for su(n) to so(2n + 1).

UR - http://www.scopus.com/inward/record.url?scp=85068339553&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/limit-shape-probability-measure-tensor-product-modules-bn-algebra

U2 - 10.1007/s10958-019-04374-y

DO - 10.1007/s10958-019-04374-y

M3 - Article

AN - SCOPUS:85068339553

VL - 240

SP - 556

EP - 566

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 5

ER -

ID: 48485698