Related papers: Proving dualities for qMZVs with connected sums
Multiples zeta values (MZV's for short) in positive characteristic were introduced by Thakur as analogues of classical multiple zeta values of Euler. In this paper we give a systematic study of algebraic structures of MZV's in positive…
The $2\times 2$ Schlesinger system for the case of four regular singularities is equivalent to the Painlev\'e VI equation. The Painlev\'e VI equation can in turn be rewritten in the symmetric form of Okamoto's equation; the dependent…
We give a proof of the strange duality or rank-level duality of the WZW models of conformal blocks by extending the genus-0 result, obtained by Nakanishi-Tsuchiya in 1992, to higher genus curves via the sewing procedure. The new ingredient…
This is the first in a series of papers that deals with duality statements such as Mukai-duality (T-duality, from algebraic geometry) and the Baum-Connes conjecture (from operator $K$-theory). These dualities are expressed in terms of…
Euler's sum formula and its multi-variable and weighted generalizations form a large class of the identities of multiple zeta values. In this paper we prove a family of identities involving Bernoulli numbers and apply them to obtain…
The special values of multiple polylogarithms, which including multiple zeta values, appear some fields of mathematics and physics. Many kinds of their linear relations are investigated as well as their algebraic relations. From the…
In this paper, we study the alternating Euler $T$-sums and $\S$-sums, which are infinite series involving (alternating) odd harmonic numbers, and have similar forms and close relations to the Dirichlet beta functions. By using the method of…
We study multiple zeta values (MZVs) from the viewpoint of zeta-functions associated with the root systems which we have studied in our previous papers. In fact, the $r$-ple zeta-functions of Euler-Zagier type can be regarded as the…
We present a unified approach which gives completely elementary proofs of three weighted sum formulae for double zeta values. This approach also leads to new evaluations of sums relating to the harmonic numbers, the alternating double zeta…
Z.-W. Sun introduced three kinds of numbers: \begin{align*}S_n=\sum_{k=0}^{n}{n\choose k}^2{2k\choose k}(2k+1),\qquad s_n=\sum_{k=0}^{n}{n\choose k}^2{2k\choose k}\frac{1}{2k-1}, \end{align*} and $S_n^{+}=\sum_{k=0}^{n}{n\choose…
We develop a geometric approach to the regularized double shuffle relations for multiple zeta values, based on convolution of perverse sheaves on $\mathbb{C}^*$ and inspired by the approach of Deligne and Terasoma. We introduce…
We show that the dualizing sheaves of reduced simple normal crossings pairs have a canonical weight filtration in a compatible way with the one on the corresponding mixed Hodge modules by calculating the extension classes between the…
We describe a relation between Arnold's strange duality and a polar duality between the Newton polytopes which is mostly due to M.~Kobayashi. We show that this relation continues to hold for the extension of Arnold's strange duality found…
We find a dual description of the supersymmetric $SL(2, \mathbb{C})/SU(2)$ WZW model as a super-winding condensate CFT, which follows simply from the bosonic AdS$_3$ duality found in [arXiv:2104.07233]. This duality can be seen as a…
In this note, we prove two supercongruences involving Almkvist--Zudilin sequences, which were originally conjectured by Z.-H. Sun.
The sum formula for multiple zeta values are derived, via the Mellin transform, from the Euler connection formula and the Landen connection formula for polylogarithms. These connection formulas for multiple polylogarithms will be considered…
We obtain a complete characterization of the space of matrix elements dual to the graded multiplicity space arising from fusion products of Kirillov-Reshetikhin modules over special twisted current algebras defined by Kus and Venkatesh,…
In this paper, we define some weighted sums of the alternating multiple $T$-values (AMTVs), and study several duality formulas for them by using the tools developed in our previous papers. Then we introduce the alternating version of the…
We present a systematic recipe for generating and classifying duality transformations in one-dimensional quantum lattice systems. Our construction emphasizes the role of global symmetries, including those described by (non)-abelian groups…
We analyze a new family of weighted double Hurwitz numbers that was introduced as a notable example in the context of the $x-y$ duality for logarithmic topological recursion. We use this family to systematically demonstrate, refine and…