## Nagoya Mathematical Journal

### Symmetry on linear relations for multiple zeta values

#### Abstract

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.

#### Article information

Source
Nagoya Math. J., Volume 189 (2008), 49-62.

Dates
First available in Project Euclid: 10 March 2008

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1205156910

Mathematical Reviews number (MathSciNet)
MR2396583

Zentralblatt MATH identifier
1132.11348

#### Citation

Ihara, Kentaro; Ochiai, Hiroyuki. Symmetry on linear relations for multiple zeta values. Nagoya Math. J. 189 (2008), 49--62. https://projecteuclid.org/euclid.nmj/1205156910

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