Interpolated Schur Multiple Zeta Values

Abstract

Inspired by a recent work of M. Nakasuji, O. Phuksuwan and Y. Yamasaki we combine interpolated multiple zeta values and Schur multiple zeta values into one object, which we call interpolated Schur multiple zeta values. Our main result will be a Jacobi-Trudi formula for a certain class of these new objects. This generalizes an analogous result for Schur multiple zeta values and implies algebraic relations between interpolated multiple zeta values. *

On multi-interpolated multiple zeta values

“…. , k n ) are interpolated Schur multiple zeta values, as introduced in [17], see also [1]. We note at the end, that it is possible to introduce multi-interpolated Schur multiple zeta values, unifying interpolated Schur multiple zeta values and multi-interpolated multiple zeta values: the parameters v(m), counting the vertical equalities, and h(m), counting the horizontal equalities can be refined by taking into account the values of the equal entries, leading to t v(m) ( 1 − t) h(m) (see [1], Definition 2.3); here λ denotes a given Young diagram.…”

On Multisets, Interpolated Multiple Zeta Values and Limit Laws

“…Our weighted enumeration also takes into account an additional parameter σ = σ n,k . It is defined similarly to Yamamoto [38]: σ counts the number of equalities in the nested sum representation, corresponding to the number of plus signs in (1) or (2). The weighted enumeration also has an algebraic interpretation, connecting elementary symmetric functions e k and complete symmetric functions h k ; moreover power sum p k s also appear in an alternative representation.…”

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

“…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].…”