Harmonics, invariants &the kernel of the multiplication map


3:00 PM - 4:00 PM



  • 时间: 3 pm-4 pm (Beijing Time)
  • 日期: Wednesday, April 10, 2024
  • 地点: MB441
  • 主讲人: Soo Teck Lee(National University of Singapore)


Let V=\C^n be the defining module for the general linear group \Gln=\Gln(\C), and let V* be its dual module. Consider the direct sum W=V^p\oplus (V*)^q of p copies of V and q copies of V*, and the algebra Pof polynomial functions on W.  Let H be the space of \Gln harmonic polynomials in P, and let J be the subalgebra of P consisting of all \Gln invariant polynomials. Let

m: H \otimes J \to P

be the linear map such that

m(h \otimes j)=hj      (h \in H,   j \in J.)

 It is well known that m is surjective, and if p+q\leq n, then m is also injective. In this talk, we shall describe the kernel of m for all values of n, p and q.

This is joint work with Roger Howe.


Soo Teck Lee is a professor of Mathematics at the National University of Singapore. He received his Ph.D from Yale University in 1993. His research interest is in representation theory and classical invariant theory. He has published over 30 papers in journals such as Bulletin of the American Mathematical Society, Compositio Mathematica, Advances in Mathematics, American Journal of Mathematics, etc.