scholarly journals Weyl Groups of the Extended Affine Root System $A_{1}^{(1,1)}$ and the Extended Affine $\mathfrak{sl}(2)$

1998 ◽  
Vol 21 (2) ◽  
pp. 299-310
Author(s):  
Tadayoshi TAKEBAYASHI
Keyword(s):  
Root System ◽  
Weyl Groups

Admissible Sequences for Twisted Involutions in Weyl Groups

2011 ◽  
Vol 54 (4) ◽  
pp. 663-675 ◽  
Author(s):  
Ruth Haas ◽  
Aloysius G. Helminck
Keyword(s):  
Weyl Group ◽  
Root System ◽  
Weyl Groups ◽  
One To One ◽  
Admissible Sequences

AbstractLetW be a Weyl group, Σ a set of simple reflections inW related to a basis Δ for the root system Φ associated with W and θ an involution such that θ(Δ) = Δ. We show that the set of θ- twisted involutions in W, = {w ∈ W | θ(w) = w–1} is in one to one correspondence with the set of regular involutions . The elements of are characterized by sequences in Σ which induce an ordering called the Richardson–Springer Poset. In particular, for Φ irreducible, the ascending Richardson–Springer Poset of , for nontrivial θ is identical to the descending Richardson–Springer Poset of .

scholarly journals Local finiteness of the twisted Bruhat orders on affine Weyl groups

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Weijia Wang
Keyword(s):  
Root System ◽  
Coxeter Group ◽  
Bruhat Order ◽  
Weyl Groups ◽  
Oriented Matroid ◽  
Positive System ◽  
Locally Finite ◽  
Affine Weyl Groups ◽  
Affine Weyl Group ◽  
Weak Bruhat Order

AbstractIn this paper, we investigate various properties of strong and weak twisted Bruhat orders on a Coxeter group. In particular, we prove that any twisted strong Bruhat order on an affine Weyl group is locally finite, strengthening a result of Dyer [Quotients of twisted Bruhat orders, J. Algebra163 (1994), 3, 861–879]. We also show that, for a non-finite and non-cofinite biclosed set 𝐵 in the positive system of an affine root system with rank greater than 2, the set of elements having a fixed 𝐵-twisted length is infinite. This implies that the twisted strong and weak Bruhat orders have an infinite antichain in those cases. Finally, we show that twisted weak Bruhat order can be applied to the study of the tope poset of an infinite oriented matroid arising from an affine root system.

Algorithms for Twisted Involutions in Weyl Groups

2012 ◽  
Vol 19 (02) ◽  
pp. 263-282 ◽  
Author(s):  
R. Haas ◽  
A. G. Helminck
Keyword(s):  
Root System ◽  
Conjugacy Classes ◽  
Weyl Groups ◽  
Coxeter System ◽  
Special Cases

Let (W, Σ) be a finite Coxeter system, and θ an involution such that θ (Δ) = Δ, where Δ is a basis for the root system Φ associated with W, and [Formula: see text] the set of θ-twisted involutions in W. The elements of [Formula: see text] can be characterized by sequences in Σ which induce an ordering called the Richardson-Spinger Bruhat poset. The main algorithm of this paper computes this poset. Algorithms for finding conjugacy classes, the closure of an element and special cases are also given. A basic analysis of the complexity of the main algorithm and its variations is discussed, as well experience with implementation.

scholarly journals ON PLANARITY OF GRAPHS ON WEYL GROUPS

1995 ◽  
Vol 26 (4) ◽  
pp. 361-369
Author(s):  
S. A. YOUSSEF ◽  
S. G. HULSURKAR
Keyword(s):  
Weyl Group ◽  
Root System ◽  
Infinite Number ◽  
Weyl Groups ◽  
Dimension Polynomial

A graph is constructed whose vertices are elements of a Weyl group and the edges are defined through nonvanishing of Wey!'s dimension polynomial at the point associated with two elements of the Weyl group. We study the planarity of such graphs on Weyl groups whose associated root system is irreducible. These graphs include four families of infinite number of graphs. We show that very few graphs, essentially five of them, are planar.

scholarly journals Weyl groups and vertex operator algebras generated by Ising vectors satisfying the (2B, 3C) condition

2014 ◽  
Vol 26 (06) ◽  
pp. 1450011
Author(s):  
Hsian-Yang Chen ◽  
Ching Hung Lam
Keyword(s):  
Weyl Group ◽  
Root System ◽  
Vertex Operator ◽  
Operator Algebras ◽  
Central Charge ◽  
Type A ◽  
Weyl Groups ◽  
Vertex Operator Algebras

In this paper, we construct explicitly certain moonshine type vertex operator algebras generated by a set of Ising vectors I such that (1) for any e ≠ f ∈ I, the subVOA VOA (e, f) generated by e and f is isomorphic to either U2B or U3C; and (2) the subgroup generated by the corresponding Miyamoto involutions {τe | e ∈ I} is isomorphic to the Weyl group of a root system of type An, Dn, E6, E7 or E8. The structures of the corresponding vertex operator algebras and their Griess algebras are also studied. In particular, the central charge of these vertex operator algebras are determined.

Distribution of secoiridoid glycosides in the root system of the medicinal plant Gentiana lutea L. subsp. aurantiaca

2017 ◽  
Author(s):  
Ó González-López ◽  
S Mayo ◽  
Á Rodríguez-González ◽  
G Carro-Huerga ◽  
V Suárez Villanueva ◽  
...  
Keyword(s):  
Medicinal Plant ◽  
Root System ◽  
Gentiana Lutea ◽  
Secoiridoid Glycosides

EFFECTS OF DECP PROCESSING ON THE ROOT SYSTEM OF COTTON

2019 ◽  
Vol 2 (1) ◽  
pp. 33-37
Author(s):  
Komiljon Komilov ◽  
◽  
Dilfuzakhon Komilova
Keyword(s):  
Root System

Global Genome Expression Analysis of Transcription Factors under PEG Osmotic Stress in Rice Root System

2009 ◽  
Vol 35 (6) ◽  
pp. 1030-1037 ◽  
Author(s):  
Ting-Chen MA ◽  
Rong-Jun CHEN ◽  
Rong-Rong YU ◽  
Han-Lai ZENG ◽  
Duan-Pin ZHANG
Keyword(s):  
Transcription Factors ◽  
Osmotic Stress ◽  
Root System ◽  
Expression Analysis ◽  
Rice Root ◽  
Genome Expression
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