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 -