Symmetry on linear relations for multiple zeta values

Kentaro Ihara, Hiroyuki Ochiai

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


We find a symmetry for the reflection groups in the double shuffle space of depth three. The space was introduced by Ihara, Kaneko and Zagier and consists of polynomials in three variables satisfying certain identities which are connected with the double shuffle relations for multiple zeta values. Goncharov has defined a space essentially equivalent to the double shuffle space and has calculated the dimension. In this paper we relate the structure among multiple zeta values of depth three with the invariant theory for the reflection groups and discuss the dimension of the double shuffle space in this view point.

Original languageEnglish
Pages (from-to)49-62
Number of pages14
JournalNagoya Mathematical Journal
Publication statusPublished - 2008
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


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