scholarly journals A Classification of Computational Assumptions in the Algebraic Group Model

2020 ◽  
pp. 121-151 ◽  
Author(s):  
Balthazar Bauer ◽  
Georg Fuchsbauer ◽  
Julian Loss
Keyword(s):  
Algebraic Group ◽  
Group Model

scholarly journals Spherical subgroups in simple algebraic groups

2015 ◽  
Vol 151 (7) ◽  
pp. 1288-1308
Author(s):  
Friedrich Knop ◽  
Gerhard Röhrle
Keyword(s):  
Algebraic Group ◽  
Closed Subgroup ◽  
Positive Characteristic ◽  
Dense Orbit ◽  
Simple Algebraic Group ◽  
Spherical Subgroup ◽  
Group A ◽  
General Deformation ◽  
Characteristic 2

Let $G$ be a simple algebraic group. A closed subgroup $H$ of $G$ is said to be spherical if it has a dense orbit on the flag variety $G/B$ of $G$. Reductive spherical subgroups of simple Lie groups were classified by Krämer in 1979. In 1997, Brundan showed that each example from Krämer’s list also gives rise to a spherical subgroup in the corresponding simple algebraic group in any positive characteristic. Nevertheless, up to now there has been no classification of all such instances in positive characteristic. The goal of this paper is to complete this classification. It turns out that there is only one additional instance (up to isogeny) in characteristic 2 which has no counterpart in Krämer’s classification. As one of our key tools, we prove a general deformation result for subgroup schemes that allows us to deduce the sphericality of subgroups in positive characteristic from the same property for subgroups in characteristic zero.

EQUIVARIANT HOLOMORPHIC HERMITIAN PRINCIPAL BUNDLES OVER A EUCLIDEAN SPACE

2013 ◽  
Vol 05 (03) ◽  
pp. 345-360
Author(s):  
INDRANIL BISWAS
Keyword(s):  
Euclidean Space ◽  
Vector Space ◽  
Algebraic Group ◽  
Inner Product ◽  
Complex Vector Space ◽  
Complex Vector ◽  
Principal Bundles ◽  
Isomorphism Classes ◽  
Finite Dimensional

Let V be a finite dimensional complex vector space equipped with an inner product. Let G denote the group of all affine automorphisms of V preserving the metric defined by the inner product. Let H be a connected reductive affine algebraic group defined over ℂ. We give an explicit classification of the isomorphism classes of G-equivariant holomorphic hermitian principal H-bundles over V.

Students with Behavioral Disorders: Determinants of Placement Outcomes

1994 ◽  
Vol 19 (3) ◽  
pp. 181-191 ◽  
Author(s):  
Leslie Ann Glassberg
Keyword(s):  
Discriminant Analysis ◽  
Behavioral Disorders ◽  
Externalizing Symptoms ◽  
Group Model ◽  
Behavioral Factors ◽  
Older Students ◽  
Behaviorally Disordered ◽  
Placement Decisions ◽  
Restrictive Settings

A discriminant analysis of characteristics of students with behavioral disorders in three progressively more intensive placements indicated that age at time of diagnosis was the strongest discriminating variable contributing to placement outcomes. Younger, brighter students tended to be mainstreamed and older students with more externalizing symptoms tended to be placed in more restrictive settings. This study corroborated findings of Kauffman, Cullinan, and Epstein (1987) by showing that cognitive, academic, and behavioral factors did not appear to play dominant roles in placement decisions. Results of this study also offered some confirmation of Olson, Algozzine, and Schmid's (1980) proposed classification of the behaviorally disordered into two groups rather than the three-group model often found in service deliveries.

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