Related papers: Higher Bruhat orders of types B and C

In this note we first consider a ternary matrix group related to the von Neumann regular semigroups and to the Artin braid group (in an algebraic way). The product of a special kind of ternary matrices (idempotent and of finite order)…

Let (W, S) be a Coxeter system. We investigate combinatorially certain partial orders, called extended Bruhat orders, on a (W x W)-set W(N,C), which depends on W, a subset N of S, and a component C of N. We determine the length of the…

Leading order higher-spin corrections to the linearized higher-spin black brane are analyzed in four dimensions. It is shown that the static solution that respects planar symmetry exists in the bosonic case at given order. Its higher-spin…

Reductions of higher tangent bundles of Lie groupoids provide natural examples of geometric structures which we would like to call higher algebroids. Such objects can be also constructed abstractly starting from an arbitrary almost Lie…

Given two algebras A and B, sometimes assumed to be C*-algebras, we consider the question of putting algebra or C*-algebra structures on the tensor product A\otimes B. In the C*-case, assuming B to be two-dimensonal, we characterize all…

We compare the results of our two papers with the results of the paper Aratyn H., Gomes J.F., Zimerman A.H., Higher order Painlev\'e equations and their symmetries via reductions of a class of integrable models, J. Phys. A: Math. Theor., V.…

We give new bounds on the Erdos-Szekeres theorems for convex bodies of Bisztriczky and Fejes Toth and of Pach and Toth. We derive them from a combinatorial characterization of convex position of a family of planar convex bodies. This…

This is a glossary of notions and methods related with the topological theory of collections of affine planes, including braid groups, configuration spaces, order complexes, stratified Morse theory, simplicial resolutions, complexes of…

We establish two types of characterizations for high order anisotropic Sobolev spaces. In particular, we prove high order anisotropic versions of Bourgain-Brezis- Mironescu's formula and Nguyen's formula.

In this paper, we give a survey of a geometrical theory of Jacobi forms of higher degree. And we present some geometric results and discuss some geometric problems to be investigated in the future.

This work introduces author's theory of Bruhat-Tits buildings over higher dimensional local fields. The theory is illustrated with the buildings for PGL(2) and PGL(3) for one- and two-dimensional local fields.

In a companion manuscript, we introduce a stratification of intersections of a top dimensional real Bruhat cells with another arbitrary cell. This intersection is naturally identified with a subset of the lower triangular group: these…

We shall work with the so called duality triads following kwa\'sniewski. In particular in this note we propose some extensions of them - hence we choose such special class of triads that admit - all at once - a unified combinatorial…

We state the relation between the variety of binary forms of given rank and the dual of the multiple root loci. This is a new result for the suprageneric rank, as a continuation of the work by Buczy\'nski, Han, Mella and Teitler. We…

We define notions of higher order spectra of a complex quasi-projective manifold with an action of a finite group $G$ and with a $G$-equivariant automorphism of finite order, some of their refinements and give Macdonald type equations for…

In this paper, we give some interesting identities of higher-order Bernoulli, Frobenius-Euler and Euler polynomials arising from umbral calculus. From our method of this paper, we can derive many interesting identities of special…

C$_{\lambda}$-extended oscillator algebras, where C$_{\lambda}$ is the cyclic group of order $\lambda$, are introduced and realized as generalized deformed oscillator algebras. For $\lambda=2$, they reduce to the well-known…

Supersymmetry is studied in 2+1 dimensions. In addition to the multiplets corresponding to those in 3+1 dimensions the Clifford algebra allows an extra set. When the extra chiral multiplet is included, formulating supersymmetric QED3 in the…

We revisit $R$-polynomials with introducing the new idea ``shifted $R$-polynomials" (or Bruhat weight) for all Bruhat intervals in finite Coxeter groups. Then, we apply these polynomials to weighted counting of Bruhat paths. Further, we…

This paper surveys, and in some cases generalises, many of the recent results on homomorphisms and the higher Ext groups for q-Schur algebras and for the Hecke algebra of type A. We review various results giving isomorphisms between Ext…