Naslov
On braided zeta functions

Autori
Shahn, Majid ; Tomašić, Ivan

Izvornik
Bulletin of Mathematical Sciences (1664-3607) 1 (2011), 2; 379-396

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Riemann hypothesis; Algebraic geometry; Motivic zeta function; Finite fields; Quantum groups; q-Deformation; Renormalisation; Braided category

Sažetak
We propose a braided approach to zeta-functions in q-deformed geometry, defining the zeta function for any rigid object in a ribbon braided category. We show that the zeta function of the complex n-space, viewed as the standard representation in the category of modules of U_q(sl_n) (for generic q) coincides with the zeta function of the same space considered as the n-dimensional representation in the category of U_q(sl_2) modules. 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 S^j(V) for V an irreducible representation of sl_2. We obtain functional equations for the associated generating function. We also discuss the zeta function for the standard q-deformed sphere.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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