Results 1 to 10 of about 3,662 (92)
Antilinear deformations of Coxeter groups, an application to Calogero models [PDF]
, 2010 We construct complex root spaces remaining invariant under antilinear involutions related to all Coxeter groups. We provide two alternative constructions: One is based on deformations of factors of the Coxeter element and the other based on the ...
Andreas Fring +13 more
core +4 more sources
Around Solomon's descent algebras [PDF]
, 2008 We study different problems related to the Solomon's descent algebra $\Sigma(W)$ of a finite Coxeter group $(W,S)$: positive elements, morphisms between descent algebras, Loewy length...
Bonnafé, Cédric, Pfeiffer, Götz
core +5 more sources
Richard Stanley through a crystal lens and from a random angle [PDF]
, 2014 We review Stanley's seminal work on the number of reduced words of the longest element of the symmetric group and his Stanley symmetric functions.
Schilling, Anne
core +3 more sources
Spacelike Singularities and Hidden Symmetries of Gravity [PDF]
Living Reviews in Relativity, 2008 Marc Henneaux
exaly +2 more sources
Dual involutions in finite Coxeter groups [PDF]
Communications in Algebra, 2022 There is a well-known classification of conjugacy classes of involutions in finite Coxeter groups, in terms of subsets of nodes of their Coxeter graphs. In many cases, the product of an involution with the longest element wo is again an involution.
Marcus Zibrowius
semanticscholar +1 more source
Commutation Classes of the Reduced Words for the Longest Element of Sn
Electronic Journal of Combinatorics, 2020 Using the standard Coxeter presentation for the symmetric group $\mathfrak{S}_{n}$, two reduced expressions for the same group element $\textsf{w}$ are said to be commutationally equivalent if one expression can be obtained from the other one by ...
G. Gutierres, R. Mamede, J. L. Santos
semanticscholar +1 more source
Smooth Schubert varieties and boolean complexes of involutions
Linköping Studies in Science and Technology. Licentiate Thesis, 2021 This thesis is composed of two papers both in algebraic combinatorics and Coxeter groups. InPaper I, we concentrate on smoothness of Schubert varieties indexed by involutions from finite simply laced types. We show that if a Schubert variety indexed by an
Vincent Umutabazi
semanticscholar +1 more source
ACTION OF LONGEST ELEMENT ON A HECKE ALGEBRA CELL MODULE [PDF]
, 2014 By a result of Mathas, the basis element Tw0 of the Hecke algebra of a finite Coxeter group acts in the canonical basis of a cell module as a permutation matrix times plus or minus a power of v. We generalize this result to the unequal parameter case. We
G. Lusztig
semanticscholar +1 more source
AUTOMORPHISM GROUP OF A BOTT–SAMELSON–DEMAZURE–HANSEN VARIETY [PDF]
Transformation groups, 2015 Let G be a simple algebraic group of adjoint type over the field of complex numbers, B be a Borel subgroup of G containing a maximal torus T of G, w be an element of the Weyl group W and X(w) be the Schubert variety in G/B corresponding to w. Let Z(w; i)
B. N. Chary +2 more
semanticscholar +2 more sources
Shadows in Coxeter groups [PDF]
, 2020 For a given $w$ in a Coxeter group $W$ the elements $u$ smaller than $w$ in Bruhat order can be seen as the end-alcoves of stammering galleries of type $w$ in the Coxeter complex $\Sigma$.
Graeber, Marius, Schwer, Petra
core +3 more sources