Results 1 to 10 of about 49 (39)
Symmetry of Narayana Numbers and Rowvacuation of Root Posets
Forum of Mathematics, Sigma, 2021 For a Weyl group W of rank r, the W-Catalan number is the number of antichains of the poset of positive roots, and the W-Narayana numbers refine the W-Catalan number by keeping track of the cardinalities of these antichains.
Colin Defant, Sam Hopkins
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On the systole growth in congruence quaternionic hyperbolic manifolds
Bulletin of the London Mathematical Society, Volume 54, Issue 4, Page 1265-1281, August 2022., 2022 Abstract We provide an explicit lower bound for the systole in principal congruence covers of compact quaternionic hyperbolic manifolds. We also prove the optimality of this lower bound.
Vincent Emery +2 more
wiley +1 more source
Intersecting principal Bruhat ideals and grades of simple modules [PDF]
, 2022 We prove that the grades of simple modules indexed by boolean permutations, over the incidence algebra of the symmetric group with respect to the Bruhat order, are given by Lusztig's \(\mathbf{a}\)-function. Our arguments are combinatorial, and include a
Tenner, Bridget Eileen +6 more
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Equivariant perverse sheaves on Coxeter arrangements and buildings [PDF]
Épijournal de Géométrie Algébrique, 2019 When $W$ is a finite Coxeter group acting by its reflection representation on $E$, we describe the category ${\mathsf{Perv}}_W(E_{\mathbb C}, {\mathcal{H}}_{\mathbb C})$ of $W$-equivariant perverse sheaves on $E_{\mathbb C}$, smooth with respect to the ...
Martin H. Weissman
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Harmonic differential forms for pseudo-reflection groups II. Bi-degree bounds [PDF]
, 2023 This paper studies three results that describe the structure of the super-coinvariant algebra of pseudo-reflection groups over a field of characteristic \(0\).
Wallach, Nolan R., Swanson, Joshua P.
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Generalized associahedra via brick polytopes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We generalize the brick polytope of V. Pilaud and F. Santos to spherical subword complexes for finite Coxeter groups. This construction provides polytopal realizations for a certain class of subword complexes containing all cluster complexes of finite ...
Vincent Pilaud, Christian Stump
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A sheep in wolf’s clothing: from group theory to a novel antiviral strategy
, 2022 The recent pandemic has led to a particular interest in mathematical and computational virology. I have previously given an introduction to virus structure and assembly, in particular the group theory aspect of structure and the modelling aspects of ...
Dechant, Pierre-Philippe
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Homological stability for Artin monoids
Proceedings of the London Mathematical Society, Volume 121, Issue 3, Page 537-583, September 2020., 2020 Abstract We prove that certain sequences of Artin monoids containing the braid monoid as a submonoid satisfy homological stability. When the K(π,1) conjecture holds for the associated family of Artin groups, this establishes homological stability for these groups.
Rachael Boyd
wiley +1 more source
Generic Newton points and the Newton poset in Iwahori-double cosets
Forum of Mathematics, Sigma, 2020 We consider the Newton stratification on Iwahori-double cosets in the loop group of a reductive group. We describe a group-theoretic condition on the generic Newton point, called cordiality, under which the Newton poset (that is, the index set for non ...
Elizabeth Milićević, Eva Viehmann
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Commuting involution graphs for [(A)\tilde]n [PDF]
, 2006 In this article we consider the commuting graphs of involution conjugacy classes in the affine Weyl group A~n. We show that where the graph is connected the diameter is at most 6.
Hart, Sarah, Hart, Sarah B.
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