Discrete Series of GLn Over a Finite Field. (AM-81), Volume 81 PDF Download
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Author: George Lusztig Publisher: ISBN: Category : Mathematics Languages : en Pages : 498
Book Description
In this book Professor Lusztig solves an interesting problem by entirely new methods: specifically, the use of cohomology of buildings and related complexes. The book gives an explicit construction of one distinguished member, D(V), of the discrete series of GLn (Fq), where V is the n-dimensional F-vector space on which GLn(Fq) acts. This is a p-adic representation; more precisely D(V) is a free module of rank (q--1) (q2—1)...(qn-1—1) over the ring of Witt vectors WF of F. In Chapter 1 the author studies the homology of partially ordered sets, and proves some vanishing theorems for the homology of some partially ordered sets associated to geometric structures. Chapter 2 is a study of the representation △ of the affine group over a finite field. In Chapter 3 D(V) is defined, and its restriction to parabolic subgroups is determined. In Chapter 4 the author computes the character of D(V), and shows how to obtain other members of the discrete series by applying Galois automorphisms to D(V). Applications are in Chapter 5. As one of the main applications of his study the author gives a precise analysis of a Brauer lifting of the standard representation of GLn(Fq).
Author: George Lusztig Publisher: ISBN: Category : Mathematics Languages : en Pages : 498
Book Description
In this book Professor Lusztig solves an interesting problem by entirely new methods: specifically, the use of cohomology of buildings and related complexes. The book gives an explicit construction of one distinguished member, D(V), of the discrete series of GLn (Fq), where V is the n-dimensional F-vector space on which GLn(Fq) acts. This is a p-adic representation; more precisely D(V) is a free module of rank (q--1) (q2—1)...(qn-1—1) over the ring of Witt vectors WF of F. In Chapter 1 the author studies the homology of partially ordered sets, and proves some vanishing theorems for the homology of some partially ordered sets associated to geometric structures. Chapter 2 is a study of the representation △ of the affine group over a finite field. In Chapter 3 D(V) is defined, and its restriction to parabolic subgroups is determined. In Chapter 4 the author computes the character of D(V), and shows how to obtain other members of the discrete series by applying Galois automorphisms to D(V). Applications are in Chapter 5. As one of the main applications of his study the author gives a precise analysis of a Brauer lifting of the standard representation of GLn(Fq).
Author: David O. Levine Publisher: Cornell University Press ISBN: 1501744151 Category : Education Languages : en Pages : 289
Book Description
Is higher education a right or a privilege? Who should go to college? What should they study there? These questions were hotly debated between the world wars, when an unprecedented boom in college enrollments forced Americans to struggle between their belief in the importance of educational opportunity and their desire to preserve the existing social structure. In The American College and the Culture of Aspiration, 1915–1940, David O. Levine offers the first in-depth history of higher education during this era, a period when colleges and universities became arbiters of social and economic mobility and a hierarchy of schools evolved to meet growing demands for occupational training and socialization.
Author: George Lusztig
Author: George Lusztig
Author: Karen M. Lamoree
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Author: George S. Pappas
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Author: David O. Levine