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).
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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 468, 2018, pp. 82–97.
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Nazarov, A.A., Postnova, O.V. The Limit Shape of a Probability Measure on a Tensor Product of Modules of the Bn Algebra. J Math Sci 240, 556–566 (2019). https://doi.org/10.1007/s10958-019-04374-y
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DOI: https://doi.org/10.1007/s10958-019-04374-y