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On braided zeta functions (CROSBI ID 200801)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

Shahn, Majid ; Tomašić, Ivan On braided zeta functions // Bulletin of Mathematical Sciences, 1 (2011), 2; 379-396. doi: 10.1007/s13373-011-0006-3

Podaci o odgovornosti

Shahn, Majid ; Tomašić, Ivan

engleski

On braided zeta functions

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.

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

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Podaci o izdanju

1 (2)

2011.

379-396

objavljeno

1664-3607

1664-3615

10.1007/s13373-011-0006-3

Povezanost rada

Matematika

Poveznice