Geodesic
A character on the quasi-symmetric functions coming from multiple zeta values
The electronic journal of combinatorics, Tome 15 (2008)

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Zbl EuDML
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).
DOI : 10.37236/821
Classification : 05E05, 11M32, 14J32, 57R20
Mots-clés : multiple zeta values, symmetric functions, quasi-symmetric functions, Hopf algebra 
Michael E. Hoffman. A character on the quasi-symmetric functions coming from multiple zeta values. The electronic journal of combinatorics, Tome 15 (2008). doi: 10.37236/821
@article{10_37236_821,
     author = {Michael E. Hoffman},
     title = {A character on the quasi-symmetric functions coming from multiple zeta values},
     journal = {The electronic journal of combinatorics},
     year = {2008},
     volume = {15},
     doi = {10.37236/821},
     zbl = {1163.05334},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/821/}
}
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