On braided zeta functions
On braided zeta functions
复制标题
关于编织 zeta 函数
DOI：
--
复制
发表时间：
2010
期刊：
影响因子：
--
通讯作者：
I. Tomasic
中科院分区：
文献类型：
--
作者：
S. Majid;I. Tomasic
We propose a braided approach to zeta-functions in q-deformed geometry, defining ζt for any rigid object in a ribbon braided category. We compute $${\zeta_t(\mathbb{C}^n)}$$ where $${\mathbb{C}^n}$$ is viewed as the standard representation in the category of modules of Uq(sln) and q is generic. We show that this coincides with $${\zeta_t(\mathbb{C}^n)}$$ where $${\mathbb{C}^n}$$ is the n-dimensional representation in the category of Uq(sl2) modules and that this equality of the two braided zeta functions is equivalent to the classical Cayley–Sylvester formula for the decomposition into irreducibles of the symmetric tensor products Sj(V) for V an irreducible representation of sl2. We obtain functional equations for the associated generating function. We also discuss ζt(Cq[S2]) for the standard q-deformed sphere.
We propose a braided approach to zeta-functions in q-deformed geometry, defining ζt for any rigid object in a ribbon braided category. We compute $${\zeta_t(\mathbb{C}^n)}$$ where $${\mathbb{C}^n}$$ is viewed as the standard representation in the category of modules of Uq(sln) and q is generic. We show that this coincides with $${\zeta_t(\mathbb{C}^n)}$$ where $${\mathbb{C}^n}$$ is the n-dimensional representation in the category of Uq(sl2) modules and that this equality of the two braided zeta functions is equivalent to the classical Cayley–Sylvester formula for the decomposition into irreducibles of the symmetric tensor products Sj(V) for V an irreducible representation of sl2. We obtain functional equations for the associated generating function. We also discuss ζt(Cq[S2]) for the standard q-deformed sphere.