This lecture discusses reflection groups in arbitrary characteristic.
Over the real or complex numbers, the Jacobian of the basic
invariants ties together the invariant theory and geometry in several different ways.
Over arbitrary fields, the Jacobian fails to live up to its reputation.
We show how this Jacobian defines the underlying
arrangement of reflecting hyperplanes over arbitrary fields.
Along the way, we examine the geometry of groups which fix one hyperplane
pointwise using a theory of "root vectors".

Lecture #10726

Need help? Visit our help pages at http://www.msri.org/communications/vmath/hints

Supplements

Right click on the link and "Save As..." to save to your local computer.

• 10726-Shepler.pdf (0.2 MB)

Left click on thumbnail to see a larger image.

Streaming Video

This is a high quality streaming video encoded with MPEG-4 and with 640x480 resolution.

Windows and Mac users, QuickTime 6.5 or later required
Linux users, please see our Linux Help Page on how to view our streaming videos

Follow this link to --- Watch the Video Now Via Streaming Video ---

Download QuickTime File

You can download the QuickTime file here. Right click on the link and "Save As..." to save to your local computer.

• 10726-10726-QuickTime.mov (370 MB)

Download MPEG File

You can download the MPEG file here. Right click on the link and "Save As..." to save to your local computer.

• 10726-10726-MPEG-1 DVD.mpg (746 MB)

Create a DVD

You can download the video and audio files here. Please note that you need both files to create a DVD. Right click on the link and "Save As..." to save to your local computer. You can find instructions on how to create a DVD on our help page at http://www.msri.org/communications/vmath/author

• 10726-10726-DVD PCM Audio.aiff (546 MB - Audio Only)
• 10726-10726-MPEG-2 120min High Quality Encode.m2v (1245 MB - Video Only)

Buy the DVD

If none of the options work for you, you can always buy the DVD of this lecture.

If you would like to purchase a copy of this video for $15+shipping, please Click Here!

See more of our Streaming Videos on our main VMath - Streaming Video page.