George Lusztig's Discrete Series of GLn Over a Finite Field. (AM-81) PDF

By George Lusztig

ISBN-10: 0691081549

ISBN-13: 9780691081540

In this e-book Professor Lusztig solves an enticing challenge through fullyyt new equipment: in particular, using cohomology of constructions and comparable complexes.

The e-book provides an specific building of 1 exceptional member, D(V), of the discrete sequence of GLn (Fq), the place V is the n-dimensional F-vector area on which GLn(Fq) acts. it is a p-adic illustration; extra accurately D(V) is a unfastened module of rank (q--1) (q2--1)...(qn-1--1) over the hoop of Witt vectors WF of F.

In bankruptcy 1 the writer reviews the homology of partly ordered units, and proves a few vanishing theorems for the homology of a few partly ordered units linked to geometric buildings. bankruptcy 2 is a research of the illustration ? of the affine team over a finite box. In bankruptcy three D(V) is outlined, and its limit to parabolic subgroups is decided. In bankruptcy four the writer computes the nature of D(V), and exhibits the right way to receive different participants of the discrete sequence by way of using Galois automorphisms to D(V). functions are in bankruptcy five. As one of many major purposes of his learn the writer provides an actual research of a Brauer lifting of the traditional illustration of GLn(Fq).

Show description

Read or Download Discrete Series of GLn Over a Finite Field. (AM-81) PDF

Best discrete mathematics books

Nonhomogeneous Matrix Products - download pdf or read online

Limitless items of matrices are utilized in nonhomogeneous Markov chains, Markov set-chains, demographics, probabilistic automata, construction and manpower platforms, tomography, and fractals. more moderen effects were acquired in laptop layout of curves and surfaces. This publication places jointly a lot of the elemental paintings on countless items of matrices, offering a main resource for such paintings.

New PDF release: Diskrete Mathematik

Das Standardwerk ? ber Diskrete Mathematik in deutscher Sprache. Nach 10 Jahren erscheint nun eine vollst? ndig neu bearbeitete Auflage in neuem format. Das Buch besteht aus drei Teilen: Abz? hlung, Graphen und Algorithmen, Algebraische Systeme, die weitgehend unabh? ngig voneinander gelesen werden ok?

Read e-book online Computability In Context: Computation and Logic in the Real PDF

Computability has performed a vital function in arithmetic and desktop technology, resulting in the invention, knowing and category of decidable/undecidable difficulties, paving the way in which for the fashionable desktop period, and affecting deeply our view of the area. contemporary new paradigms of computation, in line with organic and actual types, handle in a considerably new manner questions of potency and problem assumptions in regards to the so-called Turing barrier.

Download PDF by Antonella Cupillari: The Nuts and Bolts of Proofs, 3rd Edition (An Introduction

The Nuts and Bolts of evidence instructs scholars at the easy common sense of mathematical proofs, displaying how and why proofs of mathematical statements paintings. It presents them with options they could use to achieve an within view of the topic, succeed in different effects, bear in mind effects extra simply, or rederive them if the implications are forgotten.

Extra resources for Discrete Series of GLn Over a Finite Field. (AM-81)

Example text

S by the formula Here S: is any leaf of meeting E'. The map a respects the _partial order. In fact, let E', E" < SlE) such that E' C E". Assume first that E', E" E S1v(E, ). Then a(E') = = E' C E" a(E") hence a(E') S a(E"). Assume next that E', E" E S1(E) \ S1v(E, ). Let S: be a leaf meeting E'. We have a(E') = < E', f > C < E", S: > = a(E"), hence a(E') S a(E"). Finally, assume that E' E S1(E) \ S1v(E, ), E" < S1v(E, ). Then clearly a(E') E S1(E/) hence a(E') < a(E") = E" by the definition of the partial order in S(E, ).

Qn-1 _ 1 ) + q 2 . (q-1) (q -1) ... (q 1 -1) We have then n-1 X = ql+2+···+(n-1) + 2 (-l)n-iql+2+···+(i-l) i=l (qn-i+l ... ,::_ _ _-'---,_____:::__ _ ____:. 2 . (q-l)(q -1) ... (q n-1 -1) + (-l)n= 0 (q-l)(q 2 -1) ... (q 1-l) i=l and the formula for {3(n) is proved. ) In order to compute y(n), we add together the recurrence formula for y(n) with the corresponding formula in which n is replaced by n+l. Note that: (-l)nn t· (-l)n 1-1 (nt-l) = (-l)n+l and (-l)n-i (qn-i+l _l)(qn-i; 2-l) ·:· (qn-l) (q-1) (q 2 -1) ...

We shall prove that 40 aA az THE DISCRETE SERIES OF GLn OVER A FINITE FIELD is an isomorphism. Since aA = az ® lA it is sufficient to prove that is an isomorphism, and this would follow if we can prove that aA is an isomorphism whenever A is a field. Assume now that A is a field. We know that dimA He_ 1 (SI(E); A)= (q-1) (q 2 -1) · ·· (qe-1) (cf. 14) and - - - dimA He-1 (S; A)= dimA He-r--1 (SI(E/); A). dimA Hm-1 (Siv(E, ); A)= (q-1) (q2-l) ... (qe-m_l). (q -m+1 _l) (qe-m+2 _l) ... (qe-1) (cf.

Download PDF sample

Discrete Series of GLn Over a Finite Field. (AM-81) by George Lusztig

by Anthony

Rated 4.44 of 5 – based on 38 votes

About admin