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Works connected to Yasuyuki Kawahigashi

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Y. Kawahigashi: “Vaughan F. R. Jones’ achievements, I,” Sūgaku 43 : 1 (1991), pp. 29–34. MR 1111238 Zbl 0778.57001 article

V. F. R. Jones: “The Potts model and the symmetric group,” pp. 259–267 in Subfactors: Proceedings of the Taniguchi symposium on operator algebras (Kyuzeso, Japan, 6–10 July 1993). Edited by H. Araki, H. Kosaki, and Y. Kawahigashi. World Scientific (Singapore), 1994. MR 1317365 Zbl 0938.20505 incollection

The symmetric group \( S_k \) acts on a vector space \( V \) of dimension \( k \) by permuting the basis elements \( v_1,v_2 \), \( \dots,v_k \). The groups \( S_n \) acts on \( \bigotimes^n V \) by the tensor product factors. We show that the algebra of all matrices on \( \bigotimes^n V \) commuting with \( S_k \) is generated by \( S_n \) and the operators \( e_1 \) and \( e_2 \) where \begin{align*} e_1(v_{p_1}\otimes v_{p_2}\otimes \cdots \otimes v_{p_n}) &= \frac{1}{k}\sum_{i=1}^k v_i\otimes v_{p_2} \otimes\cdots\otimes v_{p_n} \\ e_2(v_{p_1} \otimes v_{p_2} \otimes \cdots \otimes v_{p_n}) &= \delta_{p_1,p_2}v_{p_1}\otimes v_{p_2}\otimes \cdots \otimes v_{p_n} \end{align*} The matrices \( e_1 \) and \( e_2 \) give the vertical and horizontal transfer matrices adding one site in the square lattice Potts model.

Yasuyuki Kawahigashi	Related
Huzihiro Araki	Related
Hideki Kosaki	Related

V. Jones: “Book review: D. Evans and Y. Kawahigashi, ‘Quantum symmetries on operator algebras’,” Bull. Am. Math. Soc. 38 : 3 (1998), pp. 369–377. article

David E. Evans	Related
Yasuyuki Kawahigashi	Related

D. Bisch, T. J. Gannon, V. F. R. Jones, and Y. Kawahigashi: “Subfactors and conformal field theory,” Oberwolfach Rep. 12 : 2 (2015), pp. 849–926. MR 3443131 Zbl 1380.00034 article

Dietmar Herbert Bisch	Related
Yasuyuki Kawahigashi	Related
Terry J. Gannon	Related