BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Hilbert's 14th problem and Verlinde type formulas for rings of inv
 ariant polynomials - Professor S. Mukai (RIMS\, Kyoto University)
DTSTART:20070130T170000Z
DTEND:20070130T180000Z
UID:TALK6450@talks.cam.ac.uk
CONTACT:4993
DESCRIPTION:I discuss the ring _R_ of polynomials which are invariant by a
  mutually commutative set of _n_ matrices.  The ring of semi-invariants of
  binary forms is an example of the case _n_=1.  For example it is generate
 d by the first coefficient and the discriminant $b^2 - 4 ac$ in the quadra
 tic case.  By Gordan and Weitzenboeck the ring _R_ is finitely generated w
 hen _n_=1.  Despite Hilbert's optimism\, _R_ is still no more finitely gen
 erated when _n_> 2.  The finite generation problem is still open in the bo
 undary case _n_=2. I present two non-trivial examples for which the answer
 s are affirmative.  Remarkably\, these examples have Verlinde type formula
 s\, which should be affine Lie algebra analogues of the classical Cayley-S
 ylvester formula.  
LOCATION:Wolfson Room (MR 2) Centre for Mathematical Sciences\, Wilberforc
 e Road\, Cambridge
END:VEVENT
END:VCALENDAR