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abstract: 'We propose a definition of equivariant (with respect to an Iwahori subgroup) $K$-theory of the formal power series model ${\mathbf{Q}_{G}}$ of semi-infinite flag manifold and prove the Pieri-Chevalley formula, which describes the product, in the $K$-theory of ${\mathbf{Q}_{G}}$, of the structure sheaf of a semi-infinite Schubert variety with a line bundle (associated to a dominant integral weight) over ${\mathbf{Q}_{G}}$. In order to achieve this, we provide a number of fundamental results on ${\mathbf{Q}_{G}}$ and its Schubert subvarieties including the Borel-Weil-Bott theory, whose special case is conjectured in [@BF14c]. One more ingredient of this paper besides the geometric results above is (a combinatorial version of) standard monomial theory for level-zero extremal weight modules over quantum affine algebras, which is described in terms of semi-infinite Lakshmibai-Seshadri paths. In fact, in our Pieri-Chevalley formula, the positivity of structure coefficients is proved by giving an explicit representation-theoretic meaning through semi-infinite Lakshmibai-Seshadri paths.'
author:
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    Syu Kato\
    Department of Mathematics, Kyoto University,\
    Oiwake Kita-Shirakawa, Sakyo, Kyoto 606-8502, Japan\
    (e-mail: [syuchan@math.kyoto-u.ac.jp]{})\
    Satoshi Naito\
    Department of Mathematics, Tokyo Institute of Technology,\
    2-12-1 Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan\
    (e-mail: [naito@math.titech.ac.jp]{})\
    and\
    Daisuke Sagaki\
    Institute of Mathematics, University of Tsukuba,\
    1-1-1 Tennodai, Tsukuba, Ibaraki 305-8571, Japan\
    