Seminar

Language English
From 2011/11/30 16:30
To 2011/11/30 17:30
PlaceRoom 110, RIMS, Kyoto University
Seminar NameColloquium
Title Parabolic Reduction, Stability and Volumes of Fundamental Domains　
Field Algebra
Geometry
Analysis
Other
SpeakersLin Weng
Affiliation九州大・数理学研究院
AbstractIn this talk, we expose an intrinsic structure of
volumes of fundamental domains for reductive groups G
defined over number fields, in terms of parabolic reduction
using stability. It claims that:

For any parabolic subgroup P of G,
let v_P=prod_M v_M denote the product of v_M,
the volumes of the fundamental domains
associated to the Levi factors M of P
and
u_P=prod_M u_M denote the product of u_M,
the volumes of moduli spaces of semistable points
associated to the Levi factors M of P,
then

v_G= sum_P c_Pu_P

and

u_G= sum_P sgn(P) e_Pv_P

with c_P and e_P non-trivial positive rational numbers,
where P runs over all standard parabolic subgroups of G.

This pair of relations is found with the help of
Arthur's analytic truncation,
Lafforgue's arithmetic truncation, and
Langlands' theory of Eisenstein series.

A beautiful formula of Kontsevich for SL(n,Z),
obtained using Harder-Narasimhan filtrations,
one of our starting points, and some examples
with lower ranks obtained by 足立憲治 will be given.
Note16:00より１階ロビーでtea

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Linkhttp://www.kurims.kyoto-u.ac.jp/ja/seminar/danwakai.html