%0 Journal Article
%T On braided zeta functions
%A Shahn Majid
%A Ivan Toma i
%J Bulletin of Mathematical Sciences
%@ 1664-3615
%D 2011
%I Springer
%R 10.1007/s13373-011-0006-3
%X We propose a braided approach to zeta-functions in q-deformed geometry, defining ¦Æ t 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 U q (sl n ) 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 U q (sl 2) modules and that this equality of the two braided zeta functions is equivalent to the classical Cayley¨CSylvester formula for the decomposition into irreducibles of the symmetric tensor products S j (V) for V an irreducible representation of sl 2. We obtain functional equations for the associated generating function. We also discuss ¦Æ t (C q [S 2]) for the standard q-deformed sphere.
%K Riemann hypothesis
%K Algebraic geometry
%K Motivic zeta function
%K Finite field
%K Quantum groups
%K q-Deformation
%K Renormalisation
%K Braided category
%K Primary 81R50
%K 58B32
%K 14G10
%U http://link.springer.com/article/10.1007/s13373-011-0006-3