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Sum formulas for Schur multiple zeta values
Journal of Combinatorial Theory Series A ( IF 1.1 ) Pub Date : 2023-07-18 , DOI: 10.1016/j.jcta.2023.105781
Henrik Bachmann , Shin-ya Kadota , Yuta Suzuki , Shuji Yamamoto , Yoshinori Yamasaki

In this paper, we study sum formulas for Schur multiple zeta values and give a generalization of the sum formulas for multiple zeta(-star) values. We show that for ribbons of certain types, the sum of Schur multiple zeta values over all admissible Young tableaux of this shape evaluates to a rational multiple of the Riemann zeta value. For arbitrary ribbons with n corners, we show that such a sum can be always expressed in terms of multiple zeta values of depth ≤n. In particular, when n=2, we give explicit, what we call, bounded type sum formulas for these ribbons. Finally, we show how to evaluate this sum when the corresponding Young diagram has exactly one corner and also prove bounded type sum formulas for them. This will also lead to relations among sums of Schur multiple zeta values over all admissible Young tableaux of different shapes.



中文翻译:

Schur 多个 zeta 值的求和公式

在本文中,我们研究了 Schur 多个 zeta 值的求和公式,并给出了多个 zeta(-star)值的求和公式的推广。我们表明,对于某些类型的丝带,该形状的所有可接受的杨氏造型的 Schur 多重 zeta 值之和等于黎曼 zeta 值的有理倍数。对于具有n 个角的任意带,我们表明这样的总和总是可以用深度 ≤ n的多个 zeta 值来表示。特别是,当n=2,我们为这些丝带给出显式的、我们所说的有界类型求和公式。最后,我们展示了当相应的杨图恰好有一个角时如何评估这个和,并证明它们的有界类型和公式。这也将导致所有可接受的不同形状的 Young 画面上的 Schur 多重 zeta 值之和之间的关系。

更新日期:2023-07-18
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