On braided zeta functions (CROSBI ID 200801)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
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