Related papers: An iterated residue perspective on stable Grothend…

Grothendieck polynomials were introduced by Lascoux and Sch\"utzenberger, and they play an important role in K-theoretic Schubert calculus. In this paper, we give a new definition of double stable Grothendieck polynomials based on an…

We prove a formula for the structure sheaf of a quiver variety in the Grothendieck ring of its embedding variety. This formula generalizes and gives new expressions for Grothendieck polynomials. We furthermore conjecture that the…

Stable Grothendieck polynomials can be viewed as a K-theory analog of Schur polynomials. We extend stable Grothendieck polynomials to a two-parameter version, which we call canonical stable Grothendieck functions. These functions have the…

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…

Quantum K-theory is a K-theoretic version of quantum cohomology, which was recently defined by Y.-P. Lee. Based on a presentation for the quantum K-theory of the classical flag variety Fl_n, we define and study quantum Grothendieck…

The flagged refined stable Grothendieck polynomials of skew shapes generalize several polynomials like stable Grothendieck polynomials, flagged skew Schur polynomials. In this paper, we provide a combinatorial expansion of the flagged…

We study the back stable $K$-theory Schubert calculus of the infinite flag variety. We define back stable (double) Grothendieck polynomials and double $K$-Stanley functions and establish coproduct expansion formulae. Applying work of…

We investigate the longstanding problem of finding a combinatorial rule for the Schubert structure constants in the $K$-theory of flag varieties (in type $A$). The Grothendieck polynomials of A. Lascoux-M.-P. Sch\"{u}tzenberger (1982) serve…

Skew stable Grothendieck polynomials are $K$-theoretic analogues of skew Schur polynomials. We give a free-fermionic presentation of skew stable Grothendieck polynomials and their dual symmetric functions. By using our presentation, we…

We formulate a nonrecursive combinatorial rule for the expansion of the stable Grothendieck polynomials of [Fomin-Kirillov '94] in the basis of stable Grothendieck polynomials for partitions. This gives a common generalization, as well as…

We provide a fermionic description of flagged skew Grothendieck polynomials, which can be seen as a $K$-theoretic counterpart of flagged skew Schur polynomials. Our proof relies on the Jacobi-Trudi type formula established by Matsumura.…

We introduce a family of tableaux that simultaneously generalizes the tableaux used to characterize Grothendieck polynomials and k-Schur functions. We prove that the polynomials drawn from these tableaux are the affine Grothendieck…

We derive explicit Pieri-type multiplication formulas in the Grothendieck ring of a flag variety. These expand the product of an arbitrary Schubert class and a special Schubert class in the basis of Schubert classes. These special Schubert…

Symmetric Grothendieck polynomials are analogues of Schur polynomials in the K-theory of Grassmannians. We build dual families of symmetric Grothendieck polynomials using Schur operators. With this approach we prove skew Cauchy identity and…

The dual stable Grothendieck polynomials are a deformation of the Schur functions, originating in the study of the K-theory of the Grassmannian. We generalize these polynomials by introducing a countable family of additional parameters, and…

Recently Galashin, Grinberg, and Liu introduced the refined dual stable Grothendieck polynomials, which are symmetric functions in $x=(x_1,x_2,\dots)$ with additional parameters $t=(t_1,t_2,\dots)$. The refined dual stable Grothendieck…

We prove an explicit combinatorial formula for the structure constants of the Grothendieck ring of a Grassmann variety with respect to its basis of Schubert structure sheaves. We furthermore relate K-theory of Grassmannians to a bialgebra…

Grothendieck polynomials, introduced by Lascoux and Sch\"utzenberger, are certain $K$-theory representatives for Schubert varieties. Symplectic Grothendieck polynomials, described more recently by Wyser and Yong, represent the $K$-theory…

Fulton's universal Schubert polynomials give cohomology formulas for a class of degeneracy loci, which generalize Schubert varieties. The K-theoretic quiver formula of Buch expresses the structure sheaves of these loci as integral linear…

The main theorem here is the K-theoretic analogue of the cohomological `stable double component formula' for quiver functions in [Knutson, Miller, and Shimozono, math.AG/0308142]. This K-theoretic version is still in terms of lacing…