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Search: MSC category 20F55 ( Reflection and Coxeter groups [See also 22E40, 51F15] )

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1. CMB 2016 (vol 59 pp. 617)

Nakashima, Norihiro; Terao, Hiroaki; Tsujie, Shuhei
 Canonical Systems of Basic Invariants for Unitary Reflection Groups It has been known that there exists a canonical system for every finite real reflection group. The first and the third authors obtained an explicit formula for a canonical system in the previous paper. In this article, we first define canonical systems for the finite unitary reflection groups, and then prove their existence. Our proof does not depend on the classification of unitary reflection groups. Furthermore, we give an explicit formula for a canonical system for every unitary reflection group. Keywords:basic invariant, invariant theory, finite unitary reflection groupCategories:13A50, 20F55

2. CMB 2010 (vol 53 pp. 602)

Boij, Mats; Geramita, Anthony
 Notes on Diagonal Coinvariants of the Dihedral Group The bigraded Hilbert function and the minimal free resolutions for the diagonal coinvariants of the dihedral groups are exhibited, as well as for all their bigraded invariant Gorenstein quotients. Categories:13D02, 20C33, 20F55

3. CMB 2009 (vol 52 pp. 435)

Monson, B.; Schulte, Egon
 Modular Reduction in Abstract Polytopes The paper studies modular reduction techniques for abstract regular and chiral polytopes, with two purposes in mind:\ first, to survey the literature about modular reduction in polytopes; and second, to apply modular reduction, with moduli given by primes in $\mathbb{Z}[\tau]$ (with $\tau$ the golden ratio), to construct new regular $4$-polytopes of hyperbolic types $\{3,5,3\}$ and $\{5,3,5\}$ with automorphism groups given by finite orthogonal groups. Keywords:abstract polytopes, regular and chiral, Coxeter groups, modular reductionCategories:51M20, 20F55

4. CMB 2007 (vol 50 pp. 535)

Hohlweg, Christophe
 Generalized Descent Algebras If $A$ is a subset of the set of reflections of a finite Coxeter group $W$, we define a sub-$\ZM$-module $\DC_A(W)$ of the group algebra $\ZM W$. We discuss cases where this submodule is a subalgebra. This family of subalgebras includes strictly the Solomon descent algebra, the group algebra and, if $W$ is of type $B$, the Mantaci--Reutenauer algebra. Keywords:Coxeter group, Solomon descent algebra, descent setCategories:20F55, 05E15

5. CMB 2005 (vol 48 pp. 460)

Sommers, Eric N.
 $B$-Stable Ideals in the Nilradical of a Borel Subalgebra We count the number of strictly positive $B$-stable ideals in the nilradical of a Borel subalgebra and prove that the minimal roots of any $B$-stable ideal are conjugate by an element of the Weyl group to a subset of the simple roots. We also count the number of ideals whose minimal roots are conjugate to a fixed subset of simple roots. Categories:20F55, 17B20, 05E99

6. CMB 2002 (vol 45 pp. 537)

Chapoton, Frédéric; Fomin, Sergey; Zelevinsky, Andrei
 Polytopal Realizations of Generalized Associahedra No abstract. Categories:05E15, 20F55, 52C07

7. CMB 1998 (vol 41 pp. 231)

Worthington, R. L.
 The growth series of compact hyperbolic Coxeter groups with 4 and 5 generators The growth series of compact hyperbolic Coxeter groups with 4 and 5 generators are explicitly calculated. The assertions of J.~Cannon and Ph.~Wagreich for the 4-generated groups, that the poles of the growth series lie on the unit circle, with the exception of a single real reciprocal pair of poles, are verified. We also verify that for the 5-generated groups, this phenomenon fails. Categories:20F05, 20F55
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