Flat matrix models for quantum permutation groups

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• 作者：Teodor Banica^a ; ^{teodor.banica@u-cergy.fr" class="auth_mail" title="E-mail the corresponding author} ; Ion Nechita^b ; ^{nechita@irsamc.ups-tlse.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：16T05 ; 46L54
• 刊名：Advances in Applied Mathematics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：83
• 期：Complete
• 页码：24-46
• 全文大小：434 K

文摘

We study the matrix models $\pi :C(S_N^{+})\to M_N(C(X))$ which are flat, in the sense that the standard generators of $C(S_N^{+})$ are mapped to rank 1 projections. Our first result is a generalization of the Pauli matrix construction at N=4$N=4$, using finite groups and 2-cocycles. Our second result is the construction of a universal representation of $C(S_N^{+})$, inspired from the Sinkhorn algorithm, that we conjecture to be inner faithful.