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Quantum invariant families of matrices in free probability |
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| Authors: | Stephen Curran Roland Speicher |
| Affiliation: | a Department of Mathematics, UCLA, Los Angeles, CA 90095, USA b Department of Mathematics and Statistics, Queen?s University, Jeffery Hall, Kingston, Ontario K7L 3N6, Canada c Saarland University, FR 6.1 - Mathematik, Campus E 2.4, 66123 Saarbrucken, Germany |
| Abstract: | We consider (self-adjoint) families of infinite matrices of noncommutative random variables such that the joint distribution of their entries is invariant under conjugation by a free quantum group. For the free orthogonal and hyperoctahedral groups, we obtain complete characterizations of the invariant families in terms of an operator-valued R-cyclicity condition. This is a surprising contrast with the Aldous-Hoover characterization of jointly exchangeable arrays. |
| Keywords: | Free probability Free quantum group Quantum invariance R-cyclic matrix |
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