A character on the quasi-symmetric functions coming from multiple zeta values (Q1010824)

Summary: We define a homomorphism \(\zeta\) from the algebra of quasi-symmetric functions to the reals which involves the Euler constant and multiple zeta values. Besides advancing the study of multiple zeta values, the homomorphism \(\zeta\) appears in connection with two Hirzebruch genera of almost complex manifolds: the \(\Gamma\)-genus (related to mirror symmetry) and the \(\hat{\Gamma}\)-genus (related to an \(S^1\)-equivariant Euler class). We decompose \(\zeta\) into its even and odd factors in the sense of Aguiar, Bergeron, and Sottille, and demonstrate the usefulness of this decomposition in computing \(\zeta\) on the subalgebra of symmetric functions (which suffices for computations of the \(\Gamma\)- and \(\hat{\Gamma}\)-genera).