Combinatorial K-theory

Anders S. Buch

To appear at Formal Power Series and Algebraic Combinatorics (FPSAC01), Tempe, Arizona (USA), May 20-26, 2001


We show that the linear span of all stable Grothendieck polynomials is a bialgebra which is a $K$-theoretic generalization of the ring of symmetric functions. We apply this bialgebra to obtain a Littlewood-Richardson rule for the $K$-theory of Grassmann varieties, as well as a formula for the structure sheaf of a quiver variety.

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