1. CJM 2007 (vol 59 pp. 742)
|Geometry and Spectra of Closed Extensions of Elliptic Cone Operators |
We study the geometry of the set of closed extensions of index $0$ of an elliptic differential cone operator and its model operator in connection with the spectra of the extensions, and we give a necessary and sufficient condition for the existence of rays of minimal growth for such operators.
Keywords:resolvents, manifolds with conical singularities, spectral theor, boundary value problems, Grassmannians
Categories:58J50, 35J70, 14M15
2. CJM 1997 (vol 49 pp. 1281)
|Pieri's formula via explicit rational equivalence |
Pieri's formula describes the intersection product of a Schubert cycle by a special Schubert cycle on a Grassmannian. We present a new geometric proof, exhibiting an explicit chain of rational equivalences from a suitable sum of distinct Schubert cycles to the intersection of a Schubert cycle with a special Schubert cycle. The geometry of these rational equivalences indicates a link to a combinatorial proof of Pieri's formula using Schensted insertion.
Keywords:Pieri's formula, rational equivalence, Grassmannian, Schensted insertion