Tetrahedron and 3D reflection equations from quantized algebra of functions
Tetrahedron and 3D reflection equations from quantized algebra of functions
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DOI：
10.1088/1751-8113/45/46/465206
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发表时间：
2012-08
期刊：
影响因子：
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通讯作者：
A. Kuniba;M. Okado
中科院分区：
文献类型：
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作者：
A. Kuniba;M. Okado
Soibelman的量子化函数代数Aq（SLn）理论提供了一个构造Zamolodchikov四面体方程解的表示理论方案。本文将Kapranov和Voevodsky的这一思想推广到Aq（Sp2n），得到了对应于四次Coxeter关系的缠绕子K。与先前已知的三维（3D）R矩阵一起，K产生了Isaev和Kulish提出的反射方程的3D模拟的第一个解。证明了R和K的矩阵元素是q中的多项式，并且R和K存在组合和双有理对应项。组合的出现要么在q = 0或通过双有理的热带化。文中还给出了B型和F4型的结构描述。
Soibelman’s theory of quantized function algebra Aq(SLn) provides a representation theoretical scheme to construct a solution of the Zamolodchikov tetrahedron equation. We extend this idea originally due to Kapranov and Voevodsky to Aq(Sp2n) and obtain the intertwiner K corresponding to the quartic Coxeter relation. Together with the previously known three-dimensional (3D) R matrix, the K yields the first ever solution to the 3D analogue of the reflection equation proposed by Isaev and Kulish. It is shown that matrix elements of R and K are polynomials in q and that there are combinatorial and birational counterparts for R and K. The combinatorial ones arise either at q = 0 or by tropicalization of the birational ones. A conjectural description for type B and F4 cases is also given.