Alladi Ramakrishnan Hall

Triple Intersection Formulas for Isotropic Grassmannians

Vijay Ravikumar

TIFR

A K-theoretic Pieri formula provides a convenient way to calculate the
product of arbitrary Schubert classes with certain special classes in the
Grothendieck ring of a homogeneous space. In this talk we calculate the
K-theoretic triple intersection numbers of Pieri type, for Grassmannians of
types B, C, and D. These can be used to quickly compute K-theoretic Pieri
coefficients, which are alternating sums of triple intersection numbers.

Our method generalizes a geometric argument used by Hodge to prove the
classical Pieri rule, and requires us to examine the projected Richardson
varieties in the underlying projective space of the Grassmannian. The
equations defining these projected Richardson varieties have applications
outside of K-theory, for example in equivariant cohomology.