On braided zeta functions

Details On braided zeta functions On braided zeta functions

2010-07-28

arxiv.org/abs/1007.5084v3

Mathematics

Quantum Algebra

16 pages, final version; added a formula for c_m(t,q)

Scientific paper

We propose a ribbon braided category approach to zeta-functions in q-deformed geometry. As a proof of concept we compute $\zeta_t(C^n)$ where $C^n$ is viewed as the standard representation in the category of modules of $U_q(sl_n)$. We show that the same $\zeta_t(C^n)$ is obtained for the $n$-dimensional representation in the category of $U_q(sl_2)$ modules. We show that this implies and is equivalent to the generating function for the decomposition into irreducibles of the symmetric tensor products $S^j(V)$ for $V$ an irreducible representation of $sl_2$. We discuss $\zeta_t(C_q(S^2))$ for the standard q-deformed sphere.

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