Lie Groups and Representation Theory

Seminar information archive ~02/27Next seminarFuture seminars 02/28~

Date, time & place Tuesday 16:30 - 18:00 126Room #126 (Graduate School of Math. Sci. Bldg.)

2012/11/06

16:30-17:30   Room #126 (Graduate School of Math. Sci. Bldg.)
Takayuki Okuda (the University of Tokyo)
An explicit construction of spherical designs on S^3 (JAPANESE)
[ Abstract ]
The existence of spherical t-designs on S^d for any t and d are proved by Seymour--Zaslavsky in 1984.
However, explicit constructions of spherical designs were not known for d > 2 and large t.
In this talk, for a given spherical t-design Y on S^2, we give an
algorithm to make a spherical 2t-design X on S^3 which maps Y by a Hopf map. In particular, by combining with the results of Kuperberg in 2005, we have an explicit construction of spherical t-designs on S^3 for any t.