论文标题
无限等级的极限形状的张量功率分解的lie代数SO（2N+1）
Limit shape for infinite rank limit of tensor power decomposition for Lie algebras of series so(2n+1)
论文作者
论文摘要
我们考虑了SO（2N+1）的旋转器表示的张量量的不可约成分的plancherel度量。不可约的表示对应于广义的年轻图。关于此度量，不可约表示的概率是其多重性和尺寸的乘积，除以张量产品的总维度。当张量功率n和代数的等级n倾向于以N/N固定为无穷大时，我们研究了广义年轻图的极限形状。我们为极限形状提供了一个明确的公式，并以概率证明了与其融合。我们证明了围绕极限形状的全局波动的中心限制定理。
We consider the Plancherel measure on irreducible components of tensor powers of the spinor representation of 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.
