FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2034453435> ?p ?o ?g. }

• W2034453435 abstract "The paper is devoted to a detailed study of some remarkable semisimple elements of (extended) Chevalley groups that are diagonalizable over the ground field — the weight elements. These are the conjugates of certain semisimple elements hω(e) of extended Chevalley groups G = G(Φ ,K ), where ω is a weight of the dual root system Φ ∨ and e ∈ K ∗ . In the adjoint case the hω(e)'s were defined by Chevalley himself and in the simply connected case they were constructed by Berman and Moody. The conjugates of hω(e) are called weight elements of type ω .V arious constructions of weight elements are discussed in the paper, in particular, their action in irreducible rational representations and weight elements induced on a regularly embedded Chevalley subgroup by the conjugation action of a larger Chevalley group. It is proved that for a given x ∈ G all elements x(e )= xhω(e)x −1 , e ∈ K ∗ ,a part maybe from a finite number of them, lie in the same Bruhat coset BwB ,w herew is an involution of the Weyl group W = W (Φ). The elements hω(e) are particularly important when ω = � i is a microweight of Φ ∨ . The main result of the paper is a calculation of the factors of the Bruhat decomposition of microweight elements x(e )f or the case whereω = � i. It turns out that all nontrivial x(e)'s lie in the same Bruhat coset BwB ,w herew is a product of reflections in pairwise strictly orthogonal roots γ1 ,...,γ r+s. Moreover, if among these roots r are long and s are short, then r +2 s does not exceed the width of the unipotent radical of the ith maximal parabolic subgroup in G. A version of this result was first announced in a paper by the author in Soviet Mathematics: Doklady in 1988. From a technical viewpoint, this amounts to the determination of Borel orbits of a Levi factor of a parabolic subgroup with Abelian unipotent radical and generalizes some results of Richardson, Rohrle, and Steinberg. These results are instrumental in the description of overgroups of a split maximal torus and in the recent papers by the author and V. Nesterov on the geometry of tori." @default.
• W2034453435 created "2016-06-24" @default.
• W2034453435 creator A5089077878 @default.
• W2034453435 date "2008-11-13" @default.
• W2034453435 modified "2023-09-27" @default.
• W2034453435 title "Weight elements of Chevalley groups" @default.
• W2034453435 cites W10983130 @default.
• W2034453435 cites W112012381 @default.
• W2034453435 cites W1503711690 @default.
• W2034453435 cites W1508601401 @default.
• W2034453435 cites W1526268882 @default.
• W2034453435 cites W1528521152 @default.
• W2034453435 cites W1537461902 @default.
• W2034453435 cites W1556069388 @default.
• W2034453435 cites W1559113333 @default.
• W2034453435 cites W1565930783 @default.
• W2034453435 cites W1584561919 @default.
• W2034453435 cites W1584901588 @default.
• W2034453435 cites W1588707588 @default.
• W2034453435 cites W1602350096 @default.
• W2034453435 cites W1958265632 @default.
• W2034453435 cites W1966611448 @default.
• W2034453435 cites W1973127708 @default.
• W2034453435 cites W1984873569 @default.
• W2034453435 cites W1995284882 @default.
• W2034453435 cites W2004239235 @default.
• W2034453435 cites W2006200341 @default.
• W2034453435 cites W2006536199 @default.
• W2034453435 cites W2007536465 @default.
• W2034453435 cites W2013185126 @default.
• W2034453435 cites W2014537434 @default.
• W2034453435 cites W2014931930 @default.
• W2034453435 cites W2016366234 @default.
• W2034453435 cites W2030065665 @default.
• W2034453435 cites W2030517170 @default.
• W2034453435 cites W2032742041 @default.
• W2034453435 cites W2035268861 @default.
• W2034453435 cites W2038883355 @default.
• W2034453435 cites W2043191398 @default.
• W2034453435 cites W2045436162 @default.
• W2034453435 cites W2045568819 @default.
• W2034453435 cites W2057347787 @default.
• W2034453435 cites W2057822652 @default.
• W2034453435 cites W2062134620 @default.
• W2034453435 cites W2069372298 @default.
• W2034453435 cites W2076033062 @default.
• W2034453435 cites W2078437137 @default.
• W2034453435 cites W2093495050 @default.
• W2034453435 cites W2095584865 @default.
• W2034453435 cites W2109496082 @default.
• W2034453435 cites W2126074275 @default.
• W2034453435 cites W2171217322 @default.
• W2034453435 cites W2171705014 @default.
• W2034453435 cites W2187714265 @default.
• W2034453435 cites W2254370513 @default.
• W2034453435 cites W2333037247 @default.
• W2034453435 cites W2583371533 @default.
• W2034453435 cites W303679994 @default.
• W2034453435 cites W3174989280 @default.
• W2034453435 cites W3190212900 @default.
• W2034453435 cites W46620492 @default.
• W2034453435 cites W563446982 @default.
• W2034453435 cites W621755548 @default.
• W2034453435 cites W623478477 @default.
• W2034453435 cites W937564869 @default.
• W2034453435 cites W998573425 @default.
• W2034453435 cites W1579430631 @default.
• W2034453435 cites W1965481605 @default.
• W2034453435 doi "https://doi.org/10.1090/s1061-0022-08-01036-4" @default.
• W2034453435 hasPublicationYear "2008" @default.
• W2034453435 type Work @default.
• W2034453435 sameAs 2034453435 @default.
• W2034453435 citedByCount "11" @default.
• W2034453435 countsByYear W20344534352012 @default.
• W2034453435 countsByYear W20344534352013 @default.
• W2034453435 countsByYear W20344534352015 @default.
• W2034453435 countsByYear W20344534352016 @default.
• W2034453435 countsByYear W20344534352017 @default.
• W2034453435 countsByYear W20344534352018 @default.
• W2034453435 crossrefType "journal-article" @default.
• W2034453435 hasAuthorship W2034453435A5089077878 @default.
• W2034453435 hasBestOaLocation W20344534351 @default.
• W2034453435 hasConcept C114411622 @default.
• W2034453435 hasConcept C114614502 @default.
• W2034453435 hasConcept C183877218 @default.
• W2034453435 hasConcept C18903297 @default.
• W2034453435 hasConcept C197893656 @default.
• W2034453435 hasConcept C202444582 @default.
• W2034453435 hasConcept C2777299769 @default.
• W2034453435 hasConcept C33923547 @default.
• W2034453435 hasConcept C5106717 @default.
• W2034453435 hasConcept C51568863 @default.
• W2034453435 hasConcept C51997251 @default.
• W2034453435 hasConcept C81651864 @default.
• W2034453435 hasConcept C85307737 @default.
• W2034453435 hasConcept C86803240 @default.
• W2034453435 hasConceptScore W2034453435C114411622 @default.
• W2034453435 hasConceptScore W2034453435C114614502 @default.
• W2034453435 hasConceptScore W2034453435C183877218 @default.
• W2034453435 hasConceptScore W2034453435C18903297 @default.

• next