The Pieri formulas and the Littlewood-Richardson rule for Schur multiple zeta functions

2023/05/31 by Shutaro Nakaoka, Nakaoka, Shutaro
Mathematics · Chemistry · #Advanced Mathematical Identities #Molecular spectroscopy and chirality #Advanced Combinatorial Mathematics

paper · pdf · doi:10.48550/arxiv.2305.19975

Abstract

We prove the Pieri formulas for Schur multiple zeta functions, which are generalizations of the Pieri formulas proved by Nakasuji and Takeda for hook type Schur multiple zeta functions. Moreover, we also prove the Littlewood-Richardson rule for Schur multiple zeta functions. In the course of their proofs, we regard the `truncated' version of Schur multiple zeta functions as series over GL(N) crystals to arrive at the Littlewood-Richardson rule for the Schur multiple zeta functions.

Related

• On Schur multiple zeta functions: A combinatoric generalization of multiple zeta functions
• Interpolated Schur multiple zeta values
• New determinant formulas of Giambelli-type for Schur multiple zeta-functions and their applications
• Shuffle product formula of the Schur multiple zeta values of hook type
• Symmetric Schur multiple zeta functions