✦ LIBER ✦

Representations of Algebraic Groups Containing Matrices with Large Jordan Blocks

✍ Scribed by Irene D. Suprunenko

Publisher: Elsevier Science
Year: 1994
Tongue: English
Weight: 185 KB
Volume: 15
Category: Article
ISSN: 0195-6698
DOI: 10.1006/eujc.1994.1010

No coin nor oath required. For personal study only.

✦ Synopsis

For a classical algebraic group (G) of rank (n), irreducible rational representations (\varphi) the images of which contain matrices with at least one Jordan block of size at least (\operatorname{dim} \varphi / n) are determined provided that the characteristic of a ground field is not equal to 2 if (G) is not of type (A_{n}). For arbitrary simple algebraic groups the question is reduced to infinitesimally irreducible representations.

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TO THE MEMORY OF MY GRANDMOTHER MARIA IVANOVNA TYSHKEVICH CONTENTS 1. Introduction. Ž . 2. Preliminary results and the general scheme of the proof of Theorem 1.1 . Ž . Ž . 3. The proof of Theorem 1.1 for G s A K . r Ž . Ž . 4. The proof of Theorem 1.1 for G s B K . r Ž . Ž . 5. The proof of Theorem