Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 25 for “"algebraic groups"”.
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Arithmetic statistics of algebraic groups
… various problems in the arithmetic statistics of algebraic groups, focusing on the distribution and properties of algebraic groups of number-theoretic interest. New results obtained throughout this thesis are unified by the development and application of methods, primarily from analytic number …
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Equivariant Embeddings of Algebraic Groups
We classify embeddings of algebraic groups as open orbits in affine varieties, generalizing results from toric geometry to connected reductive groups. In particular, we show that an embedding is determined by the set of one-parameter subgroups that have a limit in the embedding. We then investigate …
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Unipotent elements in algebraic groups
… the unipotent elements of a connected reductive algebraic group G, over an algebraically closed field k, and nilpotent elements in the Lie algebra g = LieG. The first topic is a determination of canonical forms for unipotent classes and nilpotent orbits of G. Using an original approach, we begin …
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Bounding cohomology for low rank algebraic groups
Let G be a semisimple linear algebraic group over an algebraically closed field of prime characteristic. In this thesis we outline the theory of such groups and their cohomology. We then concentrate on algebraic groups in rank 1 and 2, and prove some new results in their bounding cohomology.
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Semisimple filtrations of tilting modules for algebraic groups
Let $G$ be a reductive algebraic group over an algebraically closed field $k$ of characteristic $p > 0$. The indecomposable tilting modules $\{T(\lambda)\}$ for $G$, which are labeled by highest weight, form an important class of self-dual representations over $k$. In this thesis we investigate …
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On eigenvectors for semisimple elements in actions of algebraic groups
Let $G$ be a simple simply connected algebraic group defined over an algebraically closed field $K$ and $V$ an irreducible module defined over $K$ on which $G$ acts. Let $E$ denote the set of vectors in $V$ which are eigenvectors for some non-central semisimple element of $G$ and some eigenvalue in …
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Component Groups of Stabilizers in Algebraic Groups: Computational Methods and Applications
The component groups of the stabilizers of nilpotent elements in complex semisimple Lie algebras have been a relevant topic of research over the last century. The works of Alekseevskii (1979) and Sommers (1998) contributed significantly to the determination of such groups for exceptional Lie …
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On the Inverse Problem in Differential Galois Theory
… commute with the derivation. Differential Galois groups are linear algebraic groups over the field of constants of the base field. In analogy to the classical situation, one considers the inverse problem: Which linear algebraic groups occur as differential Galois groups over a given differential …
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Effective multiple mixing in Weyl chamber actions
… actions of semidirect products of semisimple groups with $G$-vector spaces. Using these estimates we get decay for corresponding actions in some semisimple groups of higher rank and homogeneous spaces of semidirect products of real algebraic groups.
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Analytic Continuation and Functional Equations of Cuspidal Eisenstein Series for Maximal Cuspidal Subgroups
… theory. We set up the machinery for very general algebraic groups and arithmetic subgroups, and obtain the analytic continuation and functional equations of cuspidal Eisenstein series for rank one cuspidal subgroups. This approach suggests an alternative development to part of Langlands' theory of …
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Discrete approximate subgroups of Lie groups
… of Meyer's theorem in soluble Lie groups, in amenable locally compact groups and in higher-rank semi-simple algebraic groups. Along the way, we investigate properties of closed and discrete approximate subgroups of locally compact groups in general.
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Some subvarieties of the De Concini-Procesi compactification
… compactification of semi-simple adjoint algebraic groups and some relations with other topics of algebraic groups. In chapter 1, we study the closure of the totally positive part of an adjoint group in the group compactification. One result that we obtain is the positive property of the …
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Iterative Differential Galois Theory in Positive Characteristic: A Model Theoretic Approach
… by Matzat and van der Put. Instead of taking an algebraic approach, we use the methods and framework provided by the model theory of iterative differential fields. After defining what we mean by a strongly normal extension of iterative differential fields, we prove that these extensions have good …
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Iterative Connections and Abhyankar's Conjecture
… is concerned with the problem which linear algebraic groups occur as iterative differential Galois groups of IPV-extensions with restricted singular locus. In this thesis, I prove the differential Abhyankar conjecture for connected groups and give necessary and sufficient conditions for …
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Adelic Fourier-Whittaker coefficients and the Casselman-Shalika formula
… forms that are defined on metaplectic groups. These groups are non-trivial covering groups of usual algebraic groups, and the forms defined on them are representations that respect the covering. As in the case for automorphic forms, these representations fall into a principle series, …
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Unipotente Charaktere und Zerlegungszahlen der endlichen Chevalleygruppen vom Typ F 4
… to the representation theory of finite Chevalleygroups. First we describe algorithms for explicit computation in connected reductive algebraic groups. These algorithms are well adapted to the computation in some finite subgroups, i.e., the finite groups of Lie type and their parabolic subgroups. …
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Charaktertafeln parabolischer Untergruppen der Steinbergschen Trialitätsgruppen und Anwendungen auf deren Darstellungstheorie
… the character tables of the maximal parabolic subgroups of Steinberg's triality groups. First, an algorithm is presented, based on the Steinberg presentation, for generic computations in finite groups of Lie type and connected reductive algebraic groups. Using this algorithm, the conjugacy classes …
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The Frobenius direct image of line bundles and the structure of representations
In the representation theory of semisimple algebraic groups in positive characteristic, the induced line bundles, ${\cal L}$($\lambda$), on the flag variety G/B, are important objects of study. E.g., their global sections form representations of G which are dual to the Weyl modules. In this thesis, …
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Some arithmetic Ramsey problems and inverse theorems
… arithmetic Ramsey type problems over abelian groups. This part consists of three chapters. In Chapter 2, using hypergraph containers, we study the rainbow Erdos-Rothschild problem for sum-free sets. This is joint work with Cheng, Li, Wang, and Zhou. In Chapters 3 and 4, we study the avoidance …
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Stability of the Bruhat decomposition
… decomposition, known from the theory of linear algebraic groups, was discussed by Kolotilina and Y eremin in the context of solving large sparse linear systems. We give an algorithm for computing the left Bruhat decomposition and consider its application to solving non-sparse linear systems. The …
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