Related papers: On Bott--Samelson rings for Coxeter groups

We construct Koppelman formulas on Grassmannians for forms with values in any holomorphic line bundle as well as in the tautological vector bundle and its dual. As a consequence we obtain some vanishing theorems of the Bott-Borel-Weil type.…

We develop combinatorics of parabolic double cosets in finite Coxeter groups as a follow-up of recent articles by Billey-Konvalinka-Petersen-Slofstra-Tenner and Petersen. (1) We construct a double coset system as a generalization of a…

We realise the cohomology ring of a flag manifold, more generally the coinvariant algebra of an arbitrary finite Coxeter group W, as a commutative subalgebra of a certain Nichols algebra in the Yetter-Drinfeld category over W. This gives a…

Let M be a paracompact smooth manifold of dimension n; A a Weil algebra and M^A the Weil bundle associated. We define and describe the notion of \widetilded-Poisson cohomology and of \widetilded^A -Poisson cohomology on M^A.

For a finite volume geodesic polyhedron P in hyperbolic 3-space, with the property that all interior angles between incident faces are integral submultiples of Pi, there is a naturally associated Coxeter group generated by reflections in…

We investigate a Hopf algebra structure on the cotensor coalgebra associated to a Hopf bimodule algebra which contains universal version of Clifford algebras and quantum groups as examples. It is shown to be the bosonization of the quantum…

Given a Lie algebroid with a representation, we construct a graded Lie algebra whose Maurer-Cartan elements characterize relative Rota-Baxter operators on Lie algebroids. We give the cohomology of relative Rota-Baxter operators and study…

We use representation theory and Bott's theorem to show vanishing of higher cotangent cohomology modules for the homogeneous coordinate ring of Grassmannians in the Pl\"ucker embedding. As a biproduct we answer a question of Wahl about the…

We obtain a formula for structure constants of certain variant form of Bott-Samelson classes for equivariant oriented cohomology of flag varieties. Specializing to singular cohomology/K-theory, we recover formulas of structure constants of…

The operation of tensor product of Cohomological Field Theories (or algebras over genus zero moduli operad) introduced in an earlier paper by the authors is described in full detail, and the proof of a theorem on additive relations between…

We use the toric degeneration of Bott-Samelson varieties and the description of cohomolgy of line bundles on toric varieties to deduce vanishings results for the cohomology of lines bundles on Bott-Samelson varieties.

We study the equivalence relation on the set of acyclic orientations of an undirected graph G generated by source-to-sink conversions. These conversions arise in the contexts of admissible sequences in Coxeter theory, quiver…

The purpose of this article is to show that the bivariant algebraic $A$-cobordism groups considered previously by the author are independent of the chosen base ring $A$. This result is proven by analyzing the bivariant ideal generated by…

In this paper, we introduce the notion of a noncommutative Poisson bialgebra, and establish the equivalence between matched pairs, Manin triples and noncommutative Poisson bialgebras. Using quasi-representations and the corresponding…

Let $n$ be a positive integer. The main result of this manuscript is a construction of a filtration on the cohomology ring of a regular nilpotent Hessenberg variety in $GL(n,{\mathbb{C}})/B$ such that its associated graded ring has graded…

We exploit the correspondence between twisted homology and quantum group to construct an algebra explanation of the open string kinematic numerator. In this setting the representation depends on string modes, and therefore the cohomology…

We prove that for every reductive algebraic group $H$ with centre of positive dimension and every integer $K$ there is a smooth and projective variety $X$ and an algebraic $H$-torsor $P \to X$ such that the classifying map $X \to \Bclass H$…

We compute the integer cohomology rings of the ``polygon spaces'' introduced in [Hausmann,Klyachko,Kapovich-Millson]. This is done by embedding them in certain toric varieties; the restriction map on cohomology is surjective and we…

Braid groups may be defined for every Coxeter diagram. Artin's braid group is of type A. Analogs of Temperley-Lieb, Hecke and Birman-Wenzl algebras exist for B-type. Our general hypothethis is that the braid group of B-type replaces Artin's…

We study the space of all bimodule homomorphisms $R_x\otimes_R R(\underline{t})\otimes_R R_y\to R_z\otimes_R R(\underline{t}')\otimes_R R_w$ as a one-sided module, where $R_x,R_y,R_z,R_w$ are standard twisted bimodules and…