K-classes of quiver cycles, Grothendieck polynomials, and iterated residues

Justin Allman: K-classes of quiver cycles, Grothendieck polynomials, and iterated residues (Under the direction of Richard Rimanyi) In the case of Dynkin quivers we establish a formula for the Grothendieck class of a quiver cycle as the iterated residue of a certain rational function, for which we provide an explicit combinatorial construction. Moreover, we utilize a new definition of the double stable Grothendieck polynomials due to Rimanyi and Szenes in terms of iterated residues to exhibit that the computation of quiver coefficients can be reduced to computing the coefficients in a combinatorially prescribed Laurent expansion of the aforementioned rational function. We also apply iterated residue techniques to the problem of expanding Grothendieck polynomials in the basis of Schur functions and to a conjecture of Buch regarding a set of algebraic generators for the ring of stable Grothendieck polynomials.