Flat matrix models for quantum permutation groups
نویسندگان
چکیده
منابع مشابه
Algebraic Quantum Permutation Groups
We discuss some algebraic aspects of quantum permutation groups, working over arbitrary fields. If K is any characteristic zero field, we show that there exists a universal cosemisimple Hopf algebra coacting on the diagonal algebra K: this is a refinement of Wang’s universality theorem for the (compact) quantum permutation group. We also prove a structural result for Hopf algebras having a non-...
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Associated to a finite graph X is its quantum automorphism group G(X). We prove a formula of type G(X ∗ Y ) = G(X) ∗w G(Y ), where ∗w is a free wreath product. Then we discuss representation theory of free wreath products, with the conjectural formula μ(G ∗w H) = μ(G) ⊠ μ(H), where μ is the associated spectral measure. This is verified in two situations: one using free probability techniques, t...
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A remarkable fact, discovered by Wang in [14], is that the set Xn = {1, . . . , n} has a quantum permutation group. For n = 1, 2, 3 this is the usual symmetric group Sn. However, starting from n = 4 the situation is different: for instance the dual of Z2 ∗ Z2 acts on X4. In other words, “quantum permutations” do exist. They form a compact quantum group Qn, satisfying the axioms of Woronowicz in...
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In this talk, I will describe how quantum groups serve as a useful means of expressing the monodromy of certain integrable, first order PDE’s. A fundamental, and paradigmatic result in this context is the Kohno–Drinfeld theorem. Roughly speaking, it asserts that the representations of Artin’s braid groups on n strands given by the universal R-matrix of a quantum group describe the monodromy of ...
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 2017
ISSN: 0196-8858
DOI: 10.1016/j.aam.2016.09.001