Results 31 to 40 of about 350,450 (63)
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
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 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
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Singular polynomials from orbit spaces [PDF]
, 2012 We consider the polynomial representation S(V*) of the rational Cherednik algebra H_c(W) associated to a finite Coxeter group W at constant parameter c.
Feigin, M., Silantyev, A.
core +1 more source
Hurwitz numbers for reflection groups III: Uniform formulae
Journal of the London Mathematical Society, Volume 111, Issue 3, March 2025.Abstract We give uniform formulae for the number of full reflection factorizations of a parabolic quasi‐Coxeter element in a Weyl group or complex reflection group, generalizing the formula for the genus‐0 Hurwitz numbers. This paper is the culmination of a series of three.
Theo Douvropoulos +2 more
wiley +1 more source
CAT(0) and cubulated Shephard groups
Journal of the London Mathematical Society, Volume 111, Issue 1, January 2025.Abstract Shephard groups are common generalizations of Coxeter groups, Artin groups, and graph products of cyclic groups. Their definition is similar to that of a Coxeter group, but generators may have arbitrary order rather than strictly order 2. We extend a well‐known result that Coxeter groups are CAT(0)$\mathrm{CAT}(0)$ to a class of Shephard ...
Katherine M. Goldman
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The excedance quotient of the Bruhat order, quasisymmetric varieties, and Temperley–Lieb algebras
Journal of the London Mathematical Society, Volume 110, Issue 4, October 2024.Abstract Let Rn=Q[x1,x2,…,xn]$R_n=\mathbb {Q}[x_1,x_2,\ldots ,x_n]$ be the ring of polynomials in n$n$ variables and consider the ideal ⟨QSymn+⟩⊆Rn$\langle \mathrm{QSym}_{n}^{+}\rangle \subseteq R_n$ generated by quasisymmetric polynomials without constant term. It was shown by J. C. Aval, F. Bergeron, and N. Bergeron that dim(Rn/⟨QSymn+⟩)=Cn$\dim \big
Nantel Bergeron, Lucas Gagnon
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Zero excess and minimal length in finite coxeter groups [PDF]
Let \mathcal{W} be the set of strongly real elements of W, a Coxeter group. Then for $w \in \mathcal{W}$, $e(w)$, the excess of w, is defined by $e(w) = \min min \{l(x)+l(y) - l(w)| w = xy; x^2 = y^2 =1}$.
Rowley, P.J., Hart, Sarah B.
core +5 more sources
Valuative invariants for large classes of matroids
Journal of the London Mathematical Society, Volume 110, Issue 3, September 2024.Abstract We study an operation in matroid theory that allows one to transition a given matroid into another with more bases via relaxing a stressed subset. This framework provides a new combinatorial characterization of the class of (elementary) split matroids.
Luis Ferroni, Benjamin Schröter
wiley +1 more source
The W(E6)$W(E_6)$‐invariant birational geometry of the moduli space of marked cubic surfaces
Mathematische Nachrichten, Volume 297, Issue 7, Page 2639-2666, July 2024.Abstract The moduli space Y=Y(E6)$Y = Y(E_6)$ of marked cubic surfaces is one of the most classical moduli spaces in algebraic geometry, dating back to the nineteenth‐century work of Cayley and Salmon. Modern interest in Y$Y$ was restored in the 1980s by Naruki's explicit construction of a W(E6)$W(E_6)$‐equivariant smooth projective compactification Y¯$
Nolan Schock
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