The canonical U(n_)-valued differential form is the canonical element of the tensor product of a certain subspace of the top degree part of the Orlik-Solomon algebra of the discriminantal arrangement and its dual space. Projections of the canonical differential form to different Kac-Moody algebras arise in solutions of Knizhnik-Zamolodchikov equations as well as Bethe ansatz constructions. This lecture gives explicit formulas for the projections to simple Lie algebras of type A with respect to a chosen Poincare-Birkhoff-Witt basis. As a byproduct of these formulas, one obtains non-trivial identites for rational functions with partial symmetries and poles at hyperplanes of the discriminantal arrangement.

Keywords:

Hyperplane arrangements

Lecture #10721

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.

• 10721-Steven.pdf (0.1 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.

• 10721-10721-QuickTime.mov (231 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.

• 10721-10721-MPEG-1 DVD.mpg (466 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

• 10721-10721-DVD PCM Audio.aiff (341 MB - Audio Only)
• 10721-10721-MPEG-2 120min High Quality Encode.m2v (776 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.