Checkerboard style Schur multiple zeta values and odd single zeta values

Abstract

We give explicit formulas for the recently introduced Schur multiple zeta values, which generalize multiple zeta(-star) values and which assign to a Young tableaux a real number. In this note we consider Young tableaux of various shapes, filled with alternating entries like a Checkerboard. In particular we obtain new sum representation for odd single zeta values in terms of these Schur multiple zeta values. As a special case we show that some Schur multiple zeta values of Checkerboard style, filled with 1 and 3, are given by determinants of matrices with odd single zeta values as entries.2010 Mathematics Subject Classification : 11M41, 05E05, 33C05.

Expressions of Schur multiple zeta-functions of anti-hook type by zeta-functions of root systems

“…where k = k − 1. This is actually a kind of harmonic product formulas for Schur multiple zeta-functions, which is seen in [2,Lemma 2.2]. Applying the same argument repeatedly to the Schur multiple zeta-function of anti-hook type on the right-hand side, we obtain the following relation, which is the same as (5.6):…”

“…This connects multiple zeta values and its variant multiple zeta-star values in a natural way. For recent developments in the theory of Schur multiple zeta-functions, see [1], [2] and [14].…”

Explicit Relations Between Kaneko-Yamamoto Type Multiple Zeta Values and Related Variants

“…The formula in Theorem 2.3 seems to be related to the harmonic product of Schur MZVs of anti-hook type in [10, Theorem 3.2] and the general harmonic product formula in [3,Lemma 2.2]. However, it does not seem to follow from them easily.…”

The Double Shuffle Relations for Multiple eisenstein Series

“…These span the space Z f and satisfy the index shuffle product. They can be seen as the formal analogues of the conjugated multiple zeta values defined in [BI,Definition 1.3].…”