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2020年10月23日(金) 15:00~16:30
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河野隆史氏(東京工業大学)
Inverse K-Chevalley formula for type A semi-infinite flag manifolds
The semi-infinite flag manifold associated to a connected, simply-connected simple algebraic group, is a reduced ind-scheme that is the semi-infinite analog of the (ordinary) flag manifold.
In our recent works, we studied the equivariant K-group of a semi-infinite flag manifold, and described a Chevalley formula explicitly; our Chevalley formula gives the expansion of the (tensor) product of a Schubert class and the class of a line bundle into a (possibly infinite) linear combination of Schubert classes twisted by characters of the maximal torus. The purpose of this talk is to describe the ‘‘inverse Chevalley formula’’, which gives the expansion of a Schubert class twisted by a character of the maximal torus into a finite linear combination of products of Schubert classes and line bundles.
In this talk, we give an explicit description of the inverse Chevalley formula in the case that the algebraic group is of type A and the character is an element of the Weyl group orbit of the 1st fundamental weight. This talk is based on a joint work with Satoshi Naito, Daniel Orr, and Daisuke Sagaki.