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Loop structure on equivariant K-theory of semi-infinite flag manifolds
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DOI：10.4007/annals.2025.202.3.2.png)
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Abstract
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We explain that the Pontryagin product structure on the equivariant K-group of an affine Grassmannian considered in [Lam-Schilling-Shimozono, Compos. Math. 146 (2010)] coincides with the tensor structure on the equivariant K-group of a semi-infinite flag manifold considered in [K-Naito-Sagaki, Duke Math. 169 (2020)]. Then, we construct an explicit isomorphism between the equivariant K-group of a semi-infinite flag manifold and a suitably localized equivariant quantum K-group of the corresponding flag manifold. These exhibit a new framework to understand the ring structure of equivariant quantum K-groups and the Peterson isomorphism.
Keywords:
semi-infinite flag manifolds
affine Grassmannians
quantum K -groups
Peterson isomorphism
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