Results 1 to 10 of about 417 (115)
Complex Reflection Subgroups of Real Reflection Groups
Journal of Algebra, 2000 Let \(V\) be an \(n\)-dimensional complex vector space, \(G\) an irreducible rank \(n\) complex, but not complexified, reflection group in \(V\), and \(W\) an irreducible rank \(2n\) finite real reflection group in \(_\mathbb{R} V\) such that ...
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Cyclic Sieving of Noncrossing Partitions for Complex Reflection Groups [PDF]
Annals of Combinatorics, 2011 23 pages; final version to appear in Annals of ...
David Bessis +2 more
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On partition algebras for complex reflection groups
Journal of Algebra, 2007 This article is a valuable addition to the topic of partition algebras which was first introduced by Jones and Martin. The author concentrates on the partition algebra of the symmetric group. One of the main results that this paper comes up with is the explicit decomposition of the wreath product of \(\mathbb{Z}_r\) and \(S_n\), and decomposition of ...
Rosa Orellana
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The minimal degree for a class of finite complex reflection groups
Journal of Algebra, 2010 We calculate the minimal degree for a class of finite complex reflection groups $G(p,p,q)$, for $p$ and $q$ primes and establish relationships between minimal degrees when these groups are taken in a direct product.
Neil Saunders
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NORMAL REFLECTION SUBGROUPS OF COMPLEX REFLECTION GROUPS [PDF]
Journal of the Institute of Mathematics of Jussieu, 2021 AbstractWe study normal reflection subgroups of complex reflection groups. Our approach leads to a refinement of a theorem of Orlik and Solomon to the effect that the generating function for fixed-space dimension over a reflection group is a product of linear factors involving generalised exponents.
Carlos E. Arreche, Nathan F. Williams
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Complex reflection groups and K3 surfaces I [PDF]
Épijournal de Géométrie Algébrique, 2021 We construct here many families of K3 surfaces that one can obtain as quotients of algebraic surfaces by some subgroups of the rank four complex reflection groups. We find in total 15 families with at worst $ADE$--singularities. In particular we classify
Cédric Bonnafé, Alessandra Sarti
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Reflection ordering in the imprimitive complex reflection group G(m, p, n)
上海师范大学学报. 自然科学版, 2021 Assume that m, p and n are positive integers, and p divides m. Let G(m, p, n) be an imprimitive complex refelction group. A partial ordering is introduced in the group G(m, p, n), as following reference, which is called the reflection ordering.
HONG Feifei, LI Jingjing, WANG Li
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Completely positive maps for imprimitive complex reflection groups
Karpatsʹkì Matematičnì Publìkacìï, 2021 In 1994, M. Bożejko and R. Speicher proved the existence of completely positive quasimultiplicative maps from the group algebra of Coxeter groups to the set of bounded operators.
H. Randriamaro
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Centralisers, complex reflection groups and actions in the Weyl group $$E_6$$ [PDF]
Journal of Homotopy and Related Structures, 2023 AbstractThe compact, connected Lie group $$E_6$$ E 6 admits two forms: simply connected and adjoint type. As we previously established, the Baum–Connes isomorphism relates the two Langlands dual forms, giving a duality between the equivariant K-theory of the ...
Wright, Nicholas +2 more
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$q,t$-Fuß-Catalan numbers for complex reflection groups [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 In type $A$, the $q,t$-Fuß-Catalan numbers $\mathrm{Cat}_n^{(m)}(q,t)$ can be defined as a bigraded Hilbert series of a module associated to the symmetric group $\mathcal{S}_n$.
Christian Stump
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