Infinite Analysis Seminar Tokyo

Date, time & place Saturday 13:30 - 16:00 117Room #117 (Graduate School of Math. Sci. Bldg.)

2007/12/22

13:00-16:30   Room #117 (Graduate School of Math. Sci. Bldg.)

Double Schubert polynomials for the classical Lie groups
[ Abstract ]
For each infinite series of the classical Lie groups of type $B$,
$C$ or $D$, we introduce a family of polynomials parametrized by the
elements of the corresponding Weyl group of infinite rank. These
polynomials
represent the Schubert classes in the equivariant cohomology of the
corresponding
flag variety. When indexed by maximal Grassmannian elements of the Weyl
group,
these polynomials are equal to the factorial analogues of Schur $Q$- or
$P$-functions defined earlier by Ivanov. This talk is based on joint work
with L. Mihalcea and H. Naruse.

Nichols-Woronowicz model of the K-ring of flag vaieties G/B
[ Abstract ]
We give a model of the equivariant $K$-ring $K_T(G/B)$ for
generalized flag varieties $G/B$ in the braided Hopf algebra
called Nichols-Woronowicz algebra. Our model is based on
the Chevalley-type formula for $K_T(G/B)$ due to Lenart
and Postnikov, which is described in terms of alcove paths.
We also discuss a conjecture on the model of the quantum
$K$-ring $QK(G/B)$.