On Schubert varieties of complexity one

E Lee, M Masuda, S Park - Pacific Journal of Mathematics, 2022 - msp.org
Let B be a Borel subgroup of GL n (ℂ) and 𝕋 a maximal torus contained in B. Then 𝕋 acts on
GL n (ℂ)∕ B and every Schubert variety is 𝕋-invariant. We say that a Schubert variety is of …

Richardson varieties, projected Richardson varieties and positroid varieties

DE Speyer - arXiv preprint arXiv:2303.04831, 2023 - arxiv.org
This is a survey article on Richardson varieties and their combinatorics. A Richardson
variety is the intersection, inside the flag manifold GL_n/B_+, of a Schubert cell (B_-u …

Lusztig's Quantum Root Vectors and a Dolbeault Complex for the A-Series Full Quantum Flag Manifolds

RÓ Buachalla, P Somberg - arXiv preprint arXiv:2312.13493, 2023 - arxiv.org
For the Drinfeld-Jimbo quantum enveloping algebra $ U_q (\frak {sl} _ {n+ 1}) $, we show
that the span of Lusztig's positive root vectors, with respect to Littlemann's nice reduced …

The Bruhat Order of a Finite Coxeter Group and Elnitsky Tilings

R Nicolaides, P Rowley - arXiv preprint arXiv:2407.07975, 2024 - arxiv.org
Suppose that $ W $ is a finite Coxeter group and $ W_J $ a standard parabolic subgroup of
$ W $. The main result proved here is that for any for any $ w\in W $ and reduced expression …

Algebraic and geometric properties of flag Bott–Samelson varieties and applications to representations

N Fujita, E Lee, DY Suh - Pacific Journal of Mathematics, 2020 - msp.org
We define and study flag Bott–Samelson varieties which generalize both Bott–Samelson
varieties and flag varieties. Using a birational morphism from an appropriate Bott–Samelson …

Locally finite completions of polyhedral complexes

D Coles, N Friedenberg - Discrete & Computational Geometry, 2024 - Springer
We develop a method for subdividing polyhedral complexes in a way that restricts the
possible recession cones and allows one to work with a fixed class of polyhedron. We use …

[HTML][HTML] Polyhedra and parameter spaces for matroids over valuation rings

A Fink, L Moci - Advances in Mathematics, 2019 - Elsevier
In this paper we address two of the major foundational questions in the theory of matroids
over rings. First, we provide a cryptomorphic axiomatisation, by introducing an analogue of …

On Enumerating Higher Bruhat Orders Through Deletion and Contraction

H Chau - arXiv preprint arXiv:2412.10532, 2024 - arxiv.org
The higher Bruhat orders $\mathcal {B}(n, k) $ were introduced by Manin-Schechtman to
study discriminantal hyperplane arrangements and subsequently studied by Ziegler, who …

Finite Coxeter Groups and Generalized Elnitsky Tilings

R Nicolaides, P Rowley - arXiv preprint arXiv:2111.10669, 2021 - arxiv.org
In [5], Elnitsky constructed three elegant bijections between classes of reduced words for
Type $\mathrm {A} $, $\mathrm {B} $ and $\mathrm {D} $ families of Coxeter groups and …

Subtilings of Elnitsky Tilings for Finite Irreducible Coxeter Groups

R Nicolaides, P Rowley - arXiv preprint arXiv:2106.03173, 2021 - arxiv.org
Subtilings of Elnitsky Tilings for Finite Irreducible Coxeter Groups arXiv:2106.03173v1 [math.GR]
6 Jun 2021 Page 1 Subtilings of Elnitsky Tilings for Finite Irreducible Coxeter Groups Robert …