Download e-book for kindle: Characters of Reductive Groups over a Finite Field by George Lusztig

By George Lusztig

ISBN-10: 0691083509

ISBN-13: 9780691083506

This booklet offers a class of all (complex)
irreducible representations of a reductive team with
connected centre, over a finite box. to accomplish this,
the writer makes use of etale intersection cohomology, and
detailed info on representations of Weyl

Show description

Read or Download Characters of Reductive Groups over a Finite Field PDF

Similar group theory books

New PDF release: An Account of the Theory of Crystallographic Groups

Lawsuits of the yankee Mathematical Society
Vol. sixteen, No. 6 (Dec. , 1965), pp. 1230-1236
Published by way of: American Mathematical Society
DOI: 10. 2307/2035904
Stable URL: http://www. jstor. org/stable/2035904
Page count number: 7

Download e-book for iPad: A Primer on Spectral Theory by Bernard Aupetit

This textbook presents an creation to the hot options of subharmonic capabilities and analytic multifunctions in spectral conception. subject matters contain the fundamental result of practical research, bounded operations on Banach and Hilbert areas, Banach algebras, and purposes of spectral subharmonicity.

Read e-book online Cohomology Rings of Finite Groups: With an Appendix: PDF

Workforce cohomology has a wealthy background that is going again a century or extra. Its origins are rooted in investigations of crew conception and num­ ber idea, and it grew into an necessary component to algebraic topology. within the final thirty years, workforce cohomology has constructed a strong con­ nection with finite team representations.

Additional info for Characters of Reductive Groups over a Finite Field

Example text

LEMMA. (i) Any right coset wWL ,n CW (w cW) has a unique element w 1 of minimal length (in W ). It is characterized by the property that w R+ for any L' f Rt n. 1 L' f ' (ii) If v, v' f WL n satisfy v' S v and if w 1 ' L,n f W has minimal length in w 1WLn then w 1v'Sw 1v (forthepartialorderin W)and ' (l. 1) where I is the length function of the Coxeter group (WL n' SL n). Proof. H w 1 ' f ' W has minimal length in w 1 WL·n, then E(w 1r) ' w > E(w 1) 1L' f R+ WL n. Hence, for L' f Ri, n, we have ' ' w 1L'cR-.

X ,1• LEMMA. ,n ) are characterized by the following two properties . (1. 2) X~,i/! X~,i/! = + Z[A] - linear combination of elements X~',i/! , w'< w' the coefficient of xL,,,,(w'< w) being an element of Z[A] which W,'f' is a Z-linear combination of elements a €A , where a is represented by an algebraic number in value o; all of whose complex conjugates have absolute :S Pv,(e(w)-e(w')-1). 2), follows from the definition of the intersection cohomology complex and from the purity theorem of Gabber, see [BBD].

X~ ,i/J of rank 1 over 11- 1 (93w) CL. /f(x). 0), there is a unique <1>-structure on this sheaf extended to the whole of L that has eigenvalue a on a stalk over 11- 1 c:Bw). ,n denoted aX~ 11- 1 c:Bw)) e. ,/,. 1,. Xw ,i/J. 9 1. ,n) . ,n)) . -1 where r 'w ,1, < Z[A], (w' ~ w), and rw w ,1, = [p]e(w)-ecw'). ,, ' 1'f' denotes the image of p E in A; the relation w' 'S_ w means that we Qe have the inclusion ~w' C ~w of the Zariski closures of :Bw', :Bw in :B. 5. 2) of L, we have L. 2). We shall denote rr- 1 (:Bw) CL.

Download PDF sample

Characters of Reductive Groups over a Finite Field by George Lusztig

by Christopher

Rated 4.61 of 5 – based on 41 votes