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 14 of 14 for “"classical groups"”.
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Branching from K to M for split classical groups
… from Ke to M Ke for the real split reductive groups of type Bn and Dn.
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A Constructive Proof of the Borel-Weil Theorem for Classical Groups
… and show that, at least in the case of the classical groups $G = U(n)$, $SO(n)$ and $Sp(2n)$, the Borel-Weil construction can be used to quite explicitly prove existence of an irreducible representation having highest weight $\lambda$, for each dominant integral form $\lambda$ on the Lie …
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Single-petaled K-types and Weyl group representations for classical groups
… quasi-single-petaled K-types for reductive Lie groups generalize petite K-types for split groups. First, we prove that a Weyl group algebra element represents the action of the long intertwining operator for each single-petaled K-type, and then we demonstrate that a Weyl group algebra element …
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The determination of the admissible nilpotent orbits in real classical groups
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1987.
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Rings of regular functions on spherical nilpotent orbits for complex classical groups
Let G be a classical group and let g be its Lie algebra. For a nilpotent element X E g, the ring R(Ox) of regular functions on the nilpotent orbit Ox is a G-module. In this thesis, we will decompose it into irreducible representations of G for some spherical nilpotent orbits.
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Untersuchungen zu Donovans Vermutung für klassische Gruppen
… of Morita equivalence classes ofblocks of finite groups with prescribed defect group is finite. In this thesisDonovan's conjecture is investigated for classical groups. First, a recenttheorem of Bonnafe and Rouquier is used to reduce Donovan'sconjecture for classical groups to unipotent and …
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On extending Scott modules
… the dimension of S(G,Q) is minimal for all p-subgroups Q of G. We study those Frobenius groups which are p-extendible and complete a classification of the local subgroups of the sporadic groups which are p-extendible. Furthermore, we study Scott modules associated to finite classical groups which …
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Homomorphic Images And Related Topics
… that generate two of the Mathieu sporadic groups, M<sub>11</sub> and M<sub>11</sub>, as well as some classical groups. We will prove their existences a variety of different ways, including the process of double coset enumeration, Iwasawa's Lemma, and linear fractional mappings. We will also …
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Ad-nilpotent ideals of complex and real reductive groups
… its relations with nilpotent orbits, affine Weyl groups, sign types and hyperplane arrangements. This thesis is divided into three parts. The first and second parts deal with ad-nilpotent ideals for complex reductive Lie groups. In the first part, we study the left equivalence relation of …
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SYMMETRIC PRESENTATIONS AND RELATED TOPICS
… presentations of a number of non-abelian simple groups, including the Mathieu group M<sub>12</sub>. We have given several progenitors, permutation and monomial, including 2*<sup>4</sup>:(2<sup>2</sup>:3), 2*<sup>5</sup>:D<sub>10</sub>, 2*<sup>8</sup>:((4X2).D<sub>4</sub>), …
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Hyperovals, Laguerre planes and hemisystems - an approach via symmetry
… geometries -- we employ knowledge about finite classical groups to solve long-standing problems in the area. We first look at hyperovals in finite Desarguesian projective planes. In the last 25 years a number of infinite families have been constructed. The area has seen a lot of activity, …
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Dual Pairs and Disconnected Reductive Groups
In R. Howe’s seminal paper, “Remarks on classical invariant theory,” he introduces the notion of a Lie algebra dual pair (a pair (g₁, g₂) of reductive Lie subalgebras of a Lie algebra g such that g₁ and g₂ equal each other’s centralizers in g) and the notion of a Lie group dual pair (a pair (G₁, …
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Unipotent elements in algebraic groups
… of such a form. Replacing G by any simple classical algebraic group, we thus obtain a unified approach to computing representatives for nilpotent orbits for all classical groups G. By applying Springer morphisms, this also yields representatives for the corresponding unipotent classes in G. …
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Difference equations with semisimple Galois groups in positive characteristic
… main result of this thesis is that the following groups occur as difference Galois groups over F: the special linear groups SL_n, the symplectic groups Sp_2d, the special orthogonal groups SO_n (here we have to assume q odd), and the Dickson group G_2 (in both cases q odd and even). We give …