TY - JOUR
AU1 - Horrocks, G.
AB - ON THE RELATION OF S-FUNCTIONS TO SCHUBERT VARIETIES .._, By G. HORROCKS [Received 2 February 1956.—Read 16 February 1956] 1. Introduction I T has been pointed but by Lesieur (9) tha t the formulae for the multiplica- tion of ^-functions, and the formulae for the products of Schubert conditions are formally identical, when the convention is made that meaningless con- dition symbols are t o be interpreted as zero. It may be remarked tha t this could have been pointed out at any time during the past fifty years, for the formula expressing an ^-function as a determinant whose elements are the sums of homogeneous products was discovered by Jacobi [(8), 370,11] who studied ^-functions as quotients of alternants, and the analogous formula for Schubert conditions was discovered by Giambelli [(5), 181]. It is the purpose of this note to go some way towards explaining this relationship for complex Grassmannians. I t is known—through the work of de Rham and others—that there is an isomorphism between the intersection ring on a differentiable manifold and the cdhomology ring of forms on the manifold, assuming that the inter- section ring has coefficients in an appropriate field (either the field of real 
TI - On the Relation of S‐Functions to Schubert Varieties
JF - Proceedings of the London Mathematical Society
DO - 10.1112/plms/s3-7.1.265
DA - 1957-01-01
UR - https://www.deepdyve.com/lp/wiley/on-the-relation-of-s-functions-to-schubert-varieties-nv1T8RcNDl
SP - 265
EP - 280
VL - s3-7
IS - 1
DP - DeepDyve
ER -