Results 41 to 50 of about 304 (161)
Arrangements stable under the Coxeter groups [PDF]
, 2012 Let B be a real hyperplane arrangement which is stable under the action of a Coxeter group W. Then B acts naturally on the set of chambers of B. We assume that B is disjoint from the Coxeter arrangement A=A(W) of W. In this paper, we show that the W-orbits of the set of chambers of B are in one-to-one correspondence with the chambers of C=A\cup B which
Kamiya, Hidehiko +2 more
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An extended definition of Anosov representation for relatively hyperbolic groups
Journal of Topology, Volume 19, Issue 2, June 2026.Abstract We define a new family of discrete representations of relatively hyperbolic groups which unifies many existing definitions and examples of geometrically finite behavior in higher rank. The definition includes the relative Anosov representations defined by Kapovich–Leeb and Zhu, and Zhu–Zimmer, as well as holonomy representations of various ...
Theodore Weisman
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Fortschritte der Physik, Volume 74, Issue 4, April 2026.ABSTRACT In this paper, we continue the development of the Cartan neural networks programme, launched with three previous publications, by focusing on some mathematical foundational aspects that we deem necessary for our next steps forward. The mathematical and conceptual results are diverse and span various mathematical fields, but the inspiring ...
Pietro Fré +4 more
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Random Structures &Algorithms, Volume 67, Issue 4, December 2025.ABSTRACT A finite group G$$ G $$ is mixable if a product of random elements, each chosen independently from two options, can distribute uniformly on G$$ G $$. We present conditions and obstructions to mixability. We show that 2‐groups, the symmetric groups, the simple alternating groups, several matrix and sporadic simple groups, and most finite ...
Gideon Amir +3 more
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Equivariant Hilbert and Ehrhart series under translative group actions
Journal of the London Mathematical Society, Volume 112, Issue 5, November 2025.Abstract We study representations of finite groups on Stanley–Reisner rings of simplicial complexes and on lattice points in lattice polytopes. The framework of translative group actions allows us to use the theory of proper colorings of simplicial complexes without requiring an explicit coloring to be given.
Alessio D'Alì, Emanuele Delucchi
wiley +1 more source
A generalized logarithmic module and duality of Coxeter multiarrangements [PDF]
, 2008 We introduce a new definition of a generalized logarithmic module of multiarrangements by uniting those of the logarithmic derivation and the differential modules.
Abe, Takuro, Takuro Abe
core +1 more source
Geometric realizations of the s‐weak order and its lattice quotients
Journal of the London Mathematical Society, Volume 112, Issue 3, September 2025.Abstract For an n$n$‐tuple s${\bm{s}}$ of nonnegative integers, the s${\bm{s}}$‐weak order is a lattice structure on s${\bm{s}}$‐trees, generalizing the weak order on permutations. We first describe the join irreducible elements, the canonical join representations, and the forcing order of the s${\bm{s}}$‐weak order in terms of combinatorial objects ...
Eva Philippe, Vincent Pilaud
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The characteristic polynomials of subarrangements of Coxeter arrangements
Discrete Mathematics, 1997 In \(R^n\), a subspace arrangement is a finite collection of subspaces. Such an arrangement generates an intersection lattice, and (via the Möbius function of that lattice) a characteristic polynomial. The author uses a method due to Blass and Sagan to determine and study several such polynomials.
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Coxeter transformation groups and reflection arrangements in smooth manifolds [PDF]
Journal of Homotopy and Related Structures, 2015 18 pages, 2 figures. V2: minor changes, typos fixed.
Das, Ronno, Deshpande, Priyavrat
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The Shi variety corresponding to an affine Weyl group
Bulletin of the London Mathematical Society, Volume 57, Issue 3, Page 913-940, March 2025.Abstract Let W$W$ be an irreducible Weyl group and Wa$W_a$ its affine Weyl group. In this article we show that there exists a bijection between Wa$W_a$ and the integral points of an affine variety, denoted X̂Wa$\widehat{X}_{W_a}$, which we call the Shi variety of Wa$W_a$.
Nathan Chapelier‐Laget
wiley +1 more source