Results 31 to 40 of about 304 (161)
Associahedra for finite‐type cluster algebras and minimal relations between g‐vectors
Proceedings of the London Mathematical Society, Volume 127, Issue 3, Page 513-588, September 2023., 2023 Abstract We show that the mesh mutations are the minimal relations among the g${\bm{g}}$‐vectors with respect to any initial seed in any finite‐type cluster algebra. We then use this algebraic result to derive geometric properties of the g${\bm{g}}$‐vector fan: we show that the space of all its polytopal realizations is a simplicial cone, and we then ...
Arnau Padrol +3 more
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Gaudin algebras, RSK and Calogero–Moser cells in Type A
Proceedings of the London Mathematical Society, Volume 126, Issue 5, Page 1467-1495, May 2023., 2023 Abstract We study the spectrum of a family of algebras, the inhomogeneous Gaudin algebras, acting on the n$n$‐fold tensor representation C[x1,…,xr]⊗n${\mathbb{C}}[x_1, \ldots , x_r]^{\otimes n}$ of the Lie algebra glr$\mathfrak {gl}_r$. We use the work of Halacheva–Kamnitzer–Rybnikov–Weekes to demonstrate that the Robinson–Schensted–Knuth ...
Adrien Brochier, Iain Gordon, Noah White
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A singular Coxeter presentation
Proceedings of the London Mathematical Society, Volume 126, Issue 3, Page 923-996, March 2023., 2023 Abstract We enlarge a Coxeter group into a category, with one object for each finite parabolic subgroup, encoding the combinatorics of double cosets. This category, the singular Coxeter monoid, is connected to the geometry of partial flag varieties. Our main result is a presentation of this category by generators and relations.
Ben Elias, Hankyung Ko
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Morphisms and Order Ideals of Toric Posets
Mathematics, 2016 Toric posets are in some sense a natural “cyclic” version of finite posets in that they capture the fundamental features of a partial order but without the notion of minimal or maximal elements.
Matthew Macauley
doaj +1 more source
Multiderivations of Coxeter arrangements [PDF]
Inventiones mathematicae, 2002 Let $V$ be an $\ell$-dimensional Euclidean space. Let $G \subset O(V)$ be a finite irreducible orthogonal reflection group. Let ${\cal A}$ be the corresponding Coxeter arrangement. Let $S$ be the algebra of polynomial functions on $V.$ For $H \in {\cal A}$ choose $α_H \in V^*$ such that $H = {\rm ker}(α_H).$ For each nonnegative integer $m$, define the
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Constructions of chiral polytopes of small rank [PDF]
, 2011 An abstract polytope of rank n is said to be chiral if its automorphism group has precisely two orbits on the flags, such that adjacent flags belong to distinct orbits. The present paper describes a general method for deriving new finite chiral polytopes
Egon Schulte +5 more
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Coxeter arrangements are hereditarily free
Tohoku Mathematical Journal, 1993 An arrangement is a finite set of hyperplanes of a real finite- dimensional vectorspace. Let \(L(A)\) denote the set of intersections of elements of \(A\). For \(X\in L(A)\) one has an arrangement \(A^ X:= \{X\cap H\mid H\in A\), \(X\not\subset H\}\) (restriction to \(X\)). Each hyperplane \(H\) of \(V\) defines (up to a constant) \(\alpha_ H\in V^*\) (
Orlik, Peter, Terao, Hiroaki
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The homotopy type of the polyhedral product for shifted complexes [PDF]
, 2013 We prove a conjecture of Bahri, Bendersky, Cohen and Gitler: if K is a shifted simplicial complex on n vertices,X1,...,Xn are pointed connected CW-complexes and CXi is the cone on Xi, then the polyhedral product determined by K and the pairs (C Xi , Xi )
Theriault, Stephen, Grbić, Jelena
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Irreducible circuits and Coxeter arrangements
Journal of Combinatorial Theory, Series A, 2007 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The geometry of zonotopal algebras II: Orlik–Terao algebras and Schubert varieties
Proceedings of the London Mathematical Society, Volume 132, Issue 6, June 2026.Abstract Zonotopal algebras, introduced by Postnikov–Shapiro–Shapiro, Ardila–Postnikov, and Holtz–Ron, show up in many different contexts, including approximation theory, representation theory, Donaldson–Thomas theory, and hypertoric geometry. In the first half of this paper, we construct a perfect pairing between the internal zonotopal algebra of a ...
Colin Crowley, Nicholas Proudfoot
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