Equivariant K-theory of the space of partial flags

Abstract

We use Drinfeld style generators and relations to define an algebra ${\mathfrak{U}}_n$ which is a ``$q=0$'' version of the affine quantum group of ${\mathfrak{gl}}_n.$ We then use the convolution product on the equivariant $K$-theory of varieties of pairs of partial flags in a $d$-dimensional vector space $V$ to define affine $0$-Schur algebras ${\mathbb{S}}_0^{\mathrm{aff}}(n,d)$ and to prove that for every $d$ there exists a surjective homomorphism from ${\mathfrak{U}}_n$ to ${\mathbb{S}}_0^{\mathrm{aff}}(n,d).$

47 pages; typos and mistakes fixed, exposition improved