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Author : Molly Przeworski
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (134 download)
Download or read book The Irreducible Representations of SL2(Fq) written by Molly Przeworski and published by . This book was released on 1994 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Cédric Bonnafé
Publisher : Springer Science & Business Media
ISBN 13 : 0857291572
Total Pages : 196 pages
Book Rating : 4.8/5 (572 download)
Download or read book Representations of SL2(Fq) written by Cédric Bonnafé and published by Springer Science & Business Media. This book was released on 2010-10-08 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Deligne-Lusztig theory aims to study representations of finite reductive groups by means of geometric methods, and particularly l-adic cohomology. Many excellent texts present, with different goals and perspectives, this theory in the general setting. This book focuses on the smallest non-trivial example, namely the group SL2(Fq), which not only provides the simplicity required for a complete description of the theory, but also the richness needed for illustrating the most delicate aspects. The development of Deligne-Lusztig theory was inspired by Drinfeld's example in 1974, and Representations of SL2(Fq) is based upon this example, and extends it to modular representation theory. To this end, the author makes use of fundamental results of l-adic cohomology. In order to efficiently use this machinery, a precise study of the geometric properties of the action of SL2(Fq) on the Drinfeld curve is conducted, with particular attention to the construction of quotients by various finite groups. At the end of the text, a succinct overview (without proof) of Deligne-Lusztig theory is given, as well as links to examples demonstrated in the text. With the provision of both a gentle introduction and several recent materials (for instance, Rouquier's theorem on derived equivalences of geometric nature), this book will be of use to graduate and postgraduate students, as well as researchers and lecturers with an interest in Deligne-Lusztig theory.
Author : Syvillia Ann Averett
Publisher :
ISBN 13 :
Total Pages : 60 pages
Book Rating : 4.:/5 (818 download)
Download or read book Some Representations of SL*(2,A) written by Syvillia Ann Averett and published by . This book was released on 2012 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of groups has been of interest to mathematicians since the 19th century. Although much is known about the structure of groups, many group theoretic problems remain unsolved. Representation theory allows us to employ linear algebra to solve such problems. The representation theory of linear groups over finite fields has been a particularly interesting topic. Studying these representations is of interest to mathematicians and other scientists as it relates to physics and modern number theory. In the 1960s Andre Weil introduced a method for finding a special unitary representation for symplectic groups over locally compact fields. This unitary representation is now referred to as the Weil representation. In 2010 Luis Gutiérrez, José Pantoja and Jorge Soto-Andrade were able to generalize Weil's method to a larger class of linear groups namely the *-analogue of Sl 2 . Originally, Weil constructed this unitary representation, decomposed it into irreducibles and, in this way, produced the irreducible complex representations of Sp (2n, k). Later, Shalika went in the other direction, first finding the irreducible representations and then computing their multiplicities in the Weil representation. We intend to follow Shalika's method. In this thesis we look to explore the representation theory of Sl * (2, A) where A is the direct sum of the upper and lower n x n block matrices in M (2 n, k), k a finite field. We use Wigner and Mackey's Method of Little Groups to construct these representations.
Author : D. J. Benson
Publisher : Cambridge University Press
ISBN 13 : 9780521636520
Total Pages : 296 pages
Book Rating : 4.6/5 (365 download)
Download or read book Representations and Cohomology: Volume 2, Cohomology of Groups and Modules written by D. J. Benson and published by Cambridge University Press. This book was released on 1991-08-22 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: A further introduction to modern developments in the representation theory of finite groups and associative algebras.
Author : D. Bump
Publisher : Springer
ISBN 13 : 3540390553
Total Pages : 196 pages
Book Rating : 4.5/5 (43 download)
Download or read book Automorphic Forms on GL (3,TR) written by D. Bump and published by Springer. This book was released on 2006-12-08 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Pavel I. Etingof
Publisher : American Mathematical Soc.
ISBN 13 : 0821853511
Total Pages : 240 pages
Book Rating : 4.8/5 (218 download)
Download or read book Introduction to Representation Theory written by Pavel I. Etingof and published by American Mathematical Soc.. This book was released on 2011 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory. The goal of this book is to give a ``holistic'' introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints. The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic knowledge of abstract algebra.
