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# Geometric Methods in Rep Theory Seminar- Syu Kato (Kyoto University)

## April 12 @ 4:00 pm - 5:00 pm

**Semi-infinite flag manifolds, space of maps, and quantum K-groups of flag manifolds**

**Abstract:** We first recall the Plucker relations, that yield a description of a(n open) space of maps from a projective line to a (partial) flag manifolds. Then, we observe a close relationship between Richardson varieties of semi-infinite flag manifolds and the space of stable maps from a projective line to a flag manifold. This makes us possible to describe quantum K-groups of flag manifolds with the K-group of semi-infinite flag manifolds. This talk is mainly based on arXiv:1805.01718. If time permits, we also explain a natural isomorphism between the K-groups of semi-infinite flag manifolds and that of affine Grassmannians conjectured by Lam-Li-Shimozono-Mihalcea in order to complete the picture.