scholarly journals Hyperfactored of Reflection Arrangement A�(G_25 )

2019 ◽  
Vol 30 (3) ◽  
pp. 57
Author(s):  
Raneen Sabah Haraj ◽  
Rabeaa AL-Aleyawee
Keyword(s):  
Complex Reflection ◽  
Reflection Arrangement

The purpose of this paper is to study the hyperfactored of the complex reflection arrangementA(G 25 ). Depending on the lattice of arrangement A(G 25 ), the basis of A(G 25 ) has been foundand then partitioned. Also, showed that A(G 25 ) is not hyperfactored and is not inductivelyfactored.

scholarly journals On the -problem for restrictions of complex reflection arrangements

2020 ◽  
Vol 156 (3) ◽  
pp. 526-532
Author(s):  
Nils Amend ◽  
Pierre Deligne ◽  
Gerhard Röhrle
Keyword(s):  
Reflection Group ◽  
Reflection Groups ◽  
Complex Reflection ◽  
Complex Reflection Groups ◽  
Complex Reflection Group ◽  
Reflection Arrangement

Let $W\subset \operatorname{GL}(V)$ be a complex reflection group and $\mathscr{A}(W)$ the set of the mirrors of the complex reflections in $W$. It is known that the complement $X(\mathscr{A}(W))$ of the reflection arrangement $\mathscr{A}(W)$ is a $K(\unicode[STIX]{x1D70B},1)$ space. For $Y$ an intersection of hyperplanes in $\mathscr{A}(W)$, let $X(\mathscr{A}(W)^{Y})$ be the complement in $Y$ of the hyperplanes in $\mathscr{A}(W)$ not containing $Y$. We hope that $X(\mathscr{A}(W)^{Y})$ is always a $K(\unicode[STIX]{x1D70B},1)$. We prove it in case of the monomial groups $W=G(r,p,\ell )$. Using known results, we then show that there remain only three irreducible complex reflection groups, leading to just eight such induced arrangements for which this $K(\unicode[STIX]{x1D70B},1)$ property remains to be proved.

scholarly journals Rouquier blocks of the cyclotomic Hecke algebras of G(de, e, r)

2010 ◽  
Vol 197 ◽  
pp. 175-212
Author(s):  
Maria Chlouveraki
Keyword(s):  
Infinite Series ◽  
Hecke Algebras ◽  
Weyl Groups ◽  
Reflection Groups ◽  
Complex Reflection ◽  
Complex Reflection Groups ◽  
Cyclotomic Hecke Algebras

The Rouquier blocks of the cyclotomic Hecke algebras, introduced by Rouquier, are a substitute for the families of characters defined by Lusztig for Weyl groups, which can be applied to all complex reflection groups. In this article, we determine them for the cyclotomic Hecke algebras of the groups of the infinite seriesG(de, e, r), thus completing their calculation for all complex reflection groups.

Complex reflection groups

1990 ◽  
Vol 18 (12) ◽  
pp. 3999-4029 ◽  
Author(s):  
M.C. Hughes
Keyword(s):  
Reflection Groups ◽  
Complex Reflection ◽  
Complex Reflection Groups

Behavioral Rehearsal: A Way of Talking about the Dying Process

1996 ◽  
Vol 32 (1) ◽  
pp. 63-76 ◽  
Author(s):  
Victoria T. Coffman ◽  
Stephen L. Coffman
Keyword(s):  
University Students ◽  
Student Responses ◽  
Performance Skills ◽  
Complex Reflection ◽  
Hospice Volunteers ◽  
Behavioral Rehearsal ◽  
As If

The authors suggest that theater activities can be used as a helpful approach to initiating more complex reflection about death among university students as well as hospice volunteers. Included in the article is an activity description and accompanying texts from a death-contemplation exercise which support this advocation. This performance skills activity produced serious student responses which were varied, articulate, and rich. Imagining and rehearsing death allows people to “act as if” and fantasize the circumstances surrounding one's death in a removed and relatively safe manner. These presentations can make the performance of life more meaningful, and the drama of death perhaps softer and more acceptable.

scholarly journals Euler Characteristic of the Truncated Order Complex of Generalized Noncrossing Partitions

10.37236/232 ◽  
2009 ◽  
Vol 16 (1) ◽  
Author(s):  
D. Armstrong ◽  
C. Krattenthaler
Keyword(s):  
Euler Characteristic ◽  
Order Complex ◽  
Reflection Groups ◽  
Noncrossing Partitions ◽  
Minimal Elements ◽  
Complex Reflection ◽  
Complex Reflection Groups ◽  
Phd Thesis

The purpose of this paper is to complete the study, begun in the first author's PhD thesis, of the topology of the poset of generalized noncrossing partitions associated to real reflection groups. In particular, we calculate the Euler characteristic of this poset with the maximal and minimal elements deleted. As we show, the result on the Euler characteristic extends to generalized noncrossing partitions associated to well-generated complex reflection groups.

scholarly journals Generalized Coinvariant Algebras for $G(r,1,n)$ in the Stanley-Reisner setting

10.37236/8109 ◽  
2019 ◽  
Vol 26 (3) ◽  
Author(s):  
Daniël Kroes
Keyword(s):  
Polynomial Ring ◽  
Reflection Group ◽  
Roots Of Unity ◽  
Complex Reflection ◽  
Complex Reflection Group ◽  
Positive Integers ◽  
Coinvariant Algebra

Let $r$ and $n$ be positive integers, let $G_n$ be the complex reflection group of $n \times n$ monomial matrices whose entries are $r^{\textrm{th}}$ roots of unity and let $0 \leq k \leq n$ be an integer. Recently, Haglund, Rhoades and Shimozono ($r=1$) and Chan and Rhoades ($r>1$) introduced quotients $R_{n,k}$ (for $r>1$) and $S_{n,k}$ (for $r \geq 1$) of the polynomial ring $\mathbb{C}[x_1,\ldots,x_n]$ in $n$ variables, which for $k=n$ reduce to the classical coinvariant algebra attached to $G_n$. When $n=k$ and $r=1$, Garsia and Stanton exhibited a quotient of $\mathbb{C}[\mathbf{y}_S]$ isomorphic to the coinvariant algebra, where $\mathbb{C}[\mathbf{y}_S]$ is the polynomial ring in $2^n-1$ variables whose variables are indexed by nonempty subsets $S \subseteq [n]$. In this paper, we will define analogous quotients that are isomorphic to $R_{n,k}$ and $S_{n,k}$.

Sign in / Sign up

Export Citation Format

Share Document