The Limit Shape of a Probability Measure on a Tensor Product of Modules of the Bn Algebra
- Authors: Nazarov A.A.1, Postnova O.V.2
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Affiliations:
- St.Petersburg State University
- St.Petersburg Department of Steklov Institute of Mathematics
- Issue: Vol 240, No 5 (2019)
- Pages: 556-566
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/242788
- DOI: https://doi.org/10.1007/s10958-019-04374-y
- ID: 242788
Cite item
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’s theorem for su(n) to so(2n + 1).
About the authors
A. A. Nazarov
St.Petersburg State University
Author for correspondence.
Email: antonnaz@gmail.com
Russian Federation, St.Petersburg
O. V. Postnova
St.Petersburg Department of Steklov Institute of Mathematics
Email: antonnaz@gmail.com
Russian Federation, St.Petersburg