scholarly journals On parabolic subgroups of Artin–Tits groups of spherical type

2019 ◽  
Vol 352 ◽  
pp. 572-610 ◽  
Author(s):  
María Cumplido ◽  
Volker Gebhardt ◽  
Juan González-Meneses ◽  
Bert Wiest
Keyword(s):  
Parabolic Subgroups ◽  
Spherical Type

scholarly journals Conjugacy stability of parabolic subgroups of Artin-Tits groups of spherical type

2020 ◽  
Vol 556 ◽  
pp. 621-633
Author(s):  
Matthieu Calvez ◽  
Bruno A. Cisneros de la Cruz ◽  
María Cumplido
Keyword(s):  
Parabolic Subgroups ◽  
Spherical Type

scholarly journals MULTIPLE FLAG IND-VARIETIES WITH FINITELY MANY ORBITS

2021 ◽  
Author(s):  
LUCAS FRESSE ◽  
IVAN PENKOV
Keyword(s):  
Algebraic Group ◽  
Linear Algebraic Group ◽  
Interesting Case ◽  
Analogous Problem ◽  
Restrictive Condition ◽  
Dimensional Case ◽  
Essential Difference ◽  
Parabolic Subgroups ◽  
Finite Dimensional ◽  
Finite Dimensional Case

AbstractLet G be one of the ind-groups GL(∞), O(∞), Sp(∞), and let P1, ..., Pℓ be an arbitrary set of ℓ splitting parabolic subgroups of G. We determine all such sets with the property that G acts with finitely many orbits on the ind-variety X1 × × Xℓ where Xi = G/Pi. In the case of a finite-dimensional classical linear algebraic group G, the analogous problem has been solved in a sequence of papers of Littelmann, Magyar–Weyman–Zelevinsky and Matsuki. An essential difference from the finite-dimensional case is that already for ℓ = 2, the condition that G acts on X1 × X2 with finitely many orbits is a rather restrictive condition on the pair P1, P2. We describe this condition explicitly. Using the description we tackle the most interesting case where ℓ = 3, and present the answer in the form of a table. For ℓ ≥ 4 there always are infinitely many G-orbits on X1 × × Xℓ.

A Note on Parabolic Subgroups and the Steenrod Algebra Action

2008 ◽  
Vol 15 (04) ◽  
pp. 689-698
Author(s):  
Nondas E. Kechagias
Keyword(s):  
Steenrod Algebra ◽  
Parabolic Subgroups ◽  
Generating Set ◽  
Modular Invariants ◽  
Dickson Algebra

The ring of modular invariants of parabolic subgroups has been described by Kuhn and Mitchell using Dickson algebra generators. We provide a new generating set which is closed under the Steenrod algebra action along with the relations between these elements.

Tits polygons

2022 ◽  
Vol 275 (1352) ◽  
Author(s):  
Bernhard Mühlherr ◽  
Richard Weiss ◽  
Holger Petersson
Keyword(s):  
Rational Points ◽  
Jordan Algebras ◽  
Parabolic Subgroups ◽  
Characteristic P ◽  
Arbitrary Group ◽  
Content Type ◽  
Defining Relations ◽  
Moufang Condition ◽  
Unique Vertex ◽  
Natural Way

We introduce the notion of a Tits polygon, a generalization of the notion of a Moufang polygon, and show that Tits polygons arise in a natural way from certain configurations of parabolic subgroups in an arbitrary spherical buildings satisfying the Moufang condition. We establish numerous basic properties of Tits polygons and characterize a large class of Tits hexagons in terms of Jordan algebras. We apply this classification to give a “rank  2 2 ” presentation for the group of F F -rational points of an arbitrary exceptional simple group of F F -rank at least  4 4 and to determine defining relations for the group of F F -rational points of an an arbitrary group of F F -rank  1 1 and absolute type D 4 D_4 , E 6 E_6 , E 7 E_7 or E 8 E_8 associated to the unique vertex of the Dynkin diagram that is not orthogonal to the highest root. All of these results are over a field of arbitrary characteristic.

scholarly journals PREGARSIDE MONOIDS AND GROUPS, PARABOLICITY, AMALGAMATION, AND FC PROPERTY

2013 ◽  
Vol 23 (06) ◽  
pp. 1431-1467
Author(s):  
EDDY GODELLE ◽  
LUIS PARIS
Keyword(s):  
Parabolic Subgroup ◽  
Parabolic Subgroups ◽  
Basic Study ◽  
The Family ◽  
Definition Of ◽  
Amalgamated Product

We define the notion of preGarside group slightly lightening the definition of Garside group so that all Artin–Tits groups are preGarside groups. This paper intends to give a first basic study on these groups. Firstly, we introduce the notion of parabolic subgroup, we prove that any preGarside group has a (partial) complemented presentation, and we characterize the parabolic subgroups in terms of these presentations. Afterwards we prove that the amalgamated product of two preGarside groups along a common parabolic subgroup is again a preGarside group. This enables us to define the family of preGarside groups of FC type as the smallest family of preGarside groups that contains the Garside groups and that is closed by amalgamation along parabolic subgroups. Finally, we make an algebraic and combinatorial study on FC type preGarside groups and their parabolic subgroups.

scholarly journals An investigation of the effects of variations in the radiation factor on the efficiency of dewar vessels

1926 ◽  
Vol 112 (760) ◽  
pp. 136-151
Keyword(s):  
Hot Water ◽  
Liquid Oxygen ◽  
Radiation Factor ◽  
Research Committee ◽  
Spherical Type ◽  
Glass Vessel ◽  
A Value ◽  
Dewar Vessel ◽  
Rate Of Cooling ◽  
Rate Of Evaporation

During the course of some work on Dewar vessels, which was carried out by one of us (B. L.) and S. F. Gates for the Oxygen Research Committee, a curious anomaly was noticed in the behaviour of an all-metal Dewar vessel. This was a commercial copper vessel of the usual spherical type with a long narrow neck of an alloy of low heat-conductivity; its capacity was two litres. The rate of evaporation of liquid oxygen stored in this vessel was approximately double that of liquid oxygen stored in a silvered glass flask of like capacity; but, when equal weights of hot water were put into each of the vessels, it was found that the rate of cooling of the water in the copper vessel was actually slower than in the silvered glass vessel. It appeared, then, that the copper vessel was only half as efficient as a silvered glass one of like capacity for the storage of liquid oxygen, whereas its efficiency for the storage of hot water was greater than that of the silvered glass vessel. This investigation arose out of a desire to explain the apparent anomaly. Previou work on the factors which influence the efficiency of Dewar vessels has been carried out by Dewar ('Proc. Roy. Inst.,' 1898, p. 815), Banneitz, Rhein and Kurze ('Ann. d. Phys.,' 1920, vol. 61, p. 113), and Briggs ('Proc. Roy. Soc. Edin.,' 1920, vol. 51, p. 97). These investigations have dealt with the efficiency of Dewar vessels considered only as containers for liquid air or oxygen, and the above-mentioned anomaly has therefore not been noticed. Briggs ( loc. cit .) worked with vessels with the vacuum-adjacent surfaces of polished gilding metal (95 per cent. copper). From his results on the rates of evaporation of liquid oxygen from these vessels, he calculated a value for the emissivity of the polished surfaces which was considerably greater than that anticipated from the usually accepted value for copper. This observation is intimately connected with that of Lambert and Gates and will be referred to later.

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