Representations of Unitary Groups and Free Convolution
Representations of Unitary Groups and Free Convolution
复制标题
酉群和自由卷积的表示
DOI：
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发表时间：
1995
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影响因子：
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通讯作者：
P. Biane
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文献类型：
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作者：
P. Biane
To each finite dimensional representation of a unitary group U(n) is associated a probability measure on the set of integers, depending on the highest weights which occur in this representation. We show that asymptotically for large n and large irreducible representations of U(n) the measure associated to the tensor product of two representations, or to the restriction of a representation to a subgroup U(m) with m comparable to n, can be expressed in terms of the measures associated to the first representations by means of the notion of free convolution (namely additive free convolution for the tensor product problem and multiplicative free convolution for the restriction problem).
