Get Cohomological Induction and Unitary Representations PDF

By Anthony W. Knapp

ISBN-10: 0691037566

ISBN-13: 9780691037561

This e-book bargains a scientific treatment--the first in publication form--of the advance and use of cohomological induction to build unitary representations. George Mackey brought induction in 1950 as a true research building for passing from a unitary illustration of a closed subgroup of a in the neighborhood compact team to a unitary illustration of the entire workforce. Later a parallel building utilizing complicated research and its linked co-homology theories grew up due to paintings by means of Borel, Weil, Harish-Chandra, Bott, Langlands, Kostant, and Schmid. Cohomological induction, brought via Zuckerman, is an algebraic analog that's technically extra plausible than the complex-analysis development and ends up in a wide repertory of irreducible unitary representations of reductive Lie groups.

The booklet, that's available to scholars past the 1st yr of graduate tuition, will curiosity mathematicians and physicists who are looking to find out about and reap the benefits of the algebraic part of the illustration concept of Lie teams. Cohomological Induction and Unitary Representations develops the mandatory history in illustration conception and comprises an introductory bankruptcy of motivation, a radical therapy of the "translation principle," and 4 appendices on algebra and analysis.

Show description

Read Online or Download Cohomological Induction and Unitary Representations PDF

Similar linear books

Sadri Hassani's Mathematical Methods: For Students of Physics and Related PDF

Meant to stick with the standard introductory physics classes, this booklet has the original function of addressing the mathematical wishes of sophomores and juniors in physics, engineering and different comparable fields. Many unique, lucid, and appropriate examples from the actual sciences, difficulties on the ends of chapters, and containers to stress vital recommendations aid advisor the coed throughout the fabric.

H. F. Baker's A Locus with 25920 Linear Self-Transformations PDF

Initially released in 1946 as quantity thirty-nine within the Cambridge Tracts in arithmetic and Mathematical Physics sequence, this booklet offers a concise account relating to linear teams. Appendices also are integrated. This ebook could be of worth to a person with an curiosity in linear teams and the background of arithmetic.

Additional resources for Cohomological Induction and Unitary Representations

Example text

D e f i n i t i o n 0 . 5 2 . With (•, •) as above, suppose that the (I, L n K) module Z has an infinitesimal character A,. We say that Z or A isinthe fair range or that Z is fair (relative to q and g) if Re (A. + 5(u), a |3) > 0 for all a e A(u). We say that Z or A is weakly fair if Re(A + <5(u), a | 3) > 0 When Z = for all a e A(u). and k = k f + SL, we have (A. ' + 6 (u),a>. ' + <5(u), a) is > 0 or > 0, respectively. Whether or not Z is one-dimensional, it is not hard to see that if Z is in the good range, then Z is in the fair range.

39) Impose 3 between spaces r(H om r(t/(fl), (Aj u ) * ®V ) LnK), and take the kernel/image as a (g, K) module analog of H 0J ( G/ L, V). 25 4. ZUCKERMAN FUNCTORS Let us bring in homological algebra, temporarily assuming that L c K . 22b). 40) r(H om q(t/( 0) ,U W ) . 41) 0 —►Homq(t/(g), V)LnK —►Hom((£/(g), (a°u)* ® V)LnK —►Homi([/(g), (a ‘u)* ® V W —> • • • in the category C(g, L n K). 41) is an injective resolution of Homq(U(g), V) l kk in the category C(g, L n K). 3) The category C(q, L n K) has enough injectives.

His idea was to adapt A + (and hence the complex structure) to the parameter, making the parameter dominant. Then the degree of interest for cohomology is S = d im c (^ / T) = dimc(u n t) . Under some hypotheses Schmid proved that the natural map from L 2 cohomology in degree S into Dolbeault cohomology is one-one. 11). 31), and suppose that A0 - S0 is analytically integral for the half sum 50 of positive roots in some (or equivalently each) positive system. 33 (Bott-Borel-Weil Theorem, third form).

Download PDF sample

Cohomological Induction and Unitary Representations by Anthony W. Knapp

by Kevin

Rated 4.76 of 5 – based on 39 votes