A couple of weeks ago, Peter Woit linked to some slides by David Vogan on the orbit method in representation theory of Lie groups. The slides give some of the flavor of subject, but in PDF form are very repetitive, for reasons that are completely clear if you’ve ever attended a Powerpoint presentation with one of those remote controls that allow you to use visual effects. Much better is Vogan’s review of Kirillov’s Lectures on the Orbit Method, a book that I have taken out of the library without reading more times than I care to admit to.
This book review is a trap! The happy adventurer skips along through the thicket of representations, lured ever deeper by the clarity of orbits, and suddenly the yoga of weights opens a trap-door down down down into the madness of Grothendieck, stealthily concealed in every corner of algebraic geometry by Deligne and his cohorts from IHES.
BEWARE!
The Hodge Conjecture can be yours, they say, and all you have to do is sacrifice your sanity and first-born child!
Whee! Gack! Hoo hoo!
When I was in fifth grade, the Hodge Conjecture took my lunch money.