# 2-D Shapes Are Behind the Drapes! by Tracy Kompelien

By Tracy Kompelien

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Title: 2-D Shapes Are in the back of the Drapes!
Author: Kompelien, Tracy
Publisher: Abdo Group
Publication Date: 2006/09/01
Number of Pages: 24
Binding style: LIBRARY
Library of Congress: 2006012570

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Additional info for 2-D Shapes Are Behind the Drapes!

Example text

X) , ).. ).. K = R and then in the case where §5 that and Zi (00) /y (s) the whole s-plane. oo(i) = y .. J Still in the case where provides almost complete information on p-adic case we only know the poles of K=R Sato's theory y .. (oo); cf. loc. cit. (oo) 1. and In the Yi'(oo); cf. op. cit. J A progress will be made in this case if we can prove the "experimental theorem" in §5. We might mention that cases; cf. [44], [19], [7]. y .. J If have been computed in several s t > 1, the expressions for have turned out to be rather complicated.

K' and each multiplied by -1 -1 (1 - q ) if K = kv is a YA. We further multiply a fex) so that in the case where p-adic field, gives a positive measure on positive constant independent of fex) = x we get the normalized Haar measure on denote the so-normalized positive measure on Z'(w)(~) Then Z'(w)(~) continuous for fy Ik YA by in §l. ~' We shall and we put w(f(x»~(x)~'(x). x wlI 1k = 1, if hence 00 = w. Furthermore in the prehomogeneous case _l s Z'(w) for every g in GA and in some cases, such as Mars' case, Z(w) and Z'(w) differ by a constant we have gZ'(w) = w(v(g» factor.

The matter was great1y c1arified by Thurston's idea of bending a Fuchsian group, see Su11ivan [24] or Kourouniotis [27]. There are a number of technica1 theorems contained in this paper in addition to the main resu1ts a11uded to above. For the reader's convenience we brief1y state them in order of occurrence. Section 1 defines stab1e representations, characterizes them in terms of parabo1ic subgroups and proves they are Zariski open in Hom(f,G). A slice theorem is proved for the action of stab1e representations.