Related papers: Higher Bruhat orders of types B and C

We discuss the role of higher Segal spaces at the interface of cyclic polytopes, orientals, and higher correspondences. Along the way we review examples from algebraic K-theory, show how cyclic polytopes provide a geometric model for the…

In this paper, we construct higher-order generalizations of the $A_6^{(1)}$- and $A_4^{(1)}$-surface type $q$-Painlev\'e equations from the system of partial difference equations with the consistency around a cube property by periodic…

The q-Hermite I-Sobolev type polynomials of higher order are consider for their study. Their hypergeometric representation is provided together with further useful properties such as several structure relations which give rise to a…

For an untwisted affine Kac-Moody Lie algebra $\mathfrak{g}$ with Cartan and Borel subalgebras $\mathfrak{h} \subset \mathfrak{b} \subset \mathfrak{g}$, affine Demazure modules are certain $U(\mathfrak{b})$-submodules of the irreducible…

We examine higher-form symmetries of quantum lattice gauge theories through the lens of homotopy theory and operator algebras. We show that in the operator-algebraic approach both higher-form symmetries and 't Hooft anomalies arise from…

We study the action on the Bruhat-Tits tree of unit groups of maximal orders in certain quaternion algebras over $\mathbb{F}_q(T)$ and discuss applications to arithmetic geometry and group theory.

The notions of higher-order weighted multilinear Poincar\'e and Sobolev inequalities in Carnot groups are introduced. As an application, weighted Leibnitz-type rules in Campanato-Morrey spaces are established.

The Bruhat operads from \cite{KS} are equipped with a structure of operads with multiplication.

Very recently, Galashin, Postnikov, and Williams introduced the notion of higher secondary polytopes, generalizing the secondary polytope of Gelfand, Kapranov, and Zelevinsky. Given an $n$-point configuration $\mathcal{A}$ in…

Braces and linear cycle sets are algebraic structures playing a major role in the classification of involutive set-theoretic solutions to the Yang-Baxter equation. This paper introduces two versions of their (co)homology theories. These…

In this paper, we define Orlov-Schulman's operators $M_L$, $M_R$, and then use them to construct the additional symmetries of the bigraded Toda hierarchy (BTH). We further show that these additional symmetries form an interesting infinite…

Given a vector bundle $A\to M$ we study the geometry of the graded manifolds $T^*[k]A[1]$, including their canonical symplectic structures, compatible Q-structures and Lagrangian Q-submanifolds. We relate these graded objects to classical…

A complete classification of isotropic vector equations of the geometric type that possess higher symmetries is proposed. New examples of integrable multi-component systems of the geometric type and their auto-Backlund transformations are…

Cube categories are used to encode higher-dimensional categorical structures. They have recently gained significant attention in the community of homotopy type theory and univalent foundations, where types carry the structure of such higher…

We construct some analog of cubical Bloch's higher Chow groups. Instead of considering cycles in $X\times\mathbb A^n$ we consider varieties $Y$ over $X$ together with a distinguished element in the $n$-th exterior power of the…

Many quantum invariants of knots and 3-manifolds (e.g. Jones polynomials) are special cases of the Witten-Reshetikhin-Turaev 3D TQFT. The latter is in turn a part of a larger theory - the Crane-Yetter 4D TQFT. In this work, we compute the…

We derive new matrix representation for higher order Daehee numbers and polynomials, the higher order lambda-Daehee numbers and polynomials and the twisted lambda-Daehee numbers and polynomials of order k. This helps us to obtain simple and…

A unified treatment of both superconformal and quasisuperconformal algebras with quadratic non-linearity is given. General formulas describing their structure are found by solving the Jacobi identities. A complete classification of…

Anna Melnikov provided a parametrization of Borel orbits in the affine variety of square-zero $n \times n$ matrices by the set of involutions in the symmetric group. A related combinatorics leads to a construction a Bott-Samelson type…

We prove the conjecture that the higher Tamari orders of Dimakis and M\"uller-Hoissen coincide with the first higher Stasheff--Tamari orders. To this end, we show that the higher Tamari orders may be conceived as the image of an…