# Dualities in Refined Grothendieck Polynomials

@inproceedings{Hawkes2021DualitiesIR, title={Dualities in Refined Grothendieck Polynomials}, author={Graham Hawkes}, year={2021} }

We give new proofs of the two types of duality for Grothendieck polynomials. Our proofs extend to proofs of these dualities for the refined Grothendieck polynomials. The second of these dualities was unknown for the refined case.

#### References

SHOWING 1-10 OF 19 REFERENCES

A Littlewood-Richardson rule for dual stable Grothendieck polynomials

- Mathematics, Computer Science
- J. Comb. Theory, Ser. A
- 2017

A simple extension of the Littlewood–Richardson rule for the expansion of the corresponding dual stable Grothendieck polynomial in terms of Schur polynomials is obtained. Expand

A Littlewood-Richardson rule for theK-theory of Grassmannians

- Mathematics
- 2000

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… Expand

Combinatorial Aspects of the K-Theory of Grassmannians

- Mathematics
- 2000

Abstract. In this paper we study Grothendieck polynomials indexed by Grassmannian permutations, which are representatives for the classes corresponding to the structure sheaves of Schubert varieties… Expand

Duality and deformations of stable Grothendieck polynomials

- Mathematics
- 2016

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… Expand

Combinatorics of K-theory via a K-theoretic Poirier-Reutenauer bialgebra

- Computer Science, Mathematics
- Discret. Math.
- 2016

The K -Knuth equivalence of Buch and Samuel (2015) is used to define a K -theoretic analogue of the Poirier-Reutenauer Hopf algebra and the Littlewood-Richardson rules of Thomas and Yong are rederived. Expand

Decompositions of Grothendieck Polynomials

- Mathematics
- 2016

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.… Expand

Stable Grothendieck polynomials and K-theoretic factor sequences

- Mathematics
- 2005

We formulate a nonrecursive combinatorial rule for the expansion of the stable Grothendieck polynomials of Fomin and Kirillov (Proc Formal Power Series Alg Comb, 1994) in the basis of stable… Expand

K-theoretic crystals for set-valued tableaux of rectangular shapes

- Mathematics
- 2019

In earlier work with C. Monical (2018), we introduced the notion of a K-crystal, with applications to K-theoretic Schubert calculus and the study of Lascoux polynomials. We conjectured that such a… Expand

ON THE COMBINATORICS OF CRYSTAL GRAPHS, I. LUSZTIG'S INVOLUTION

- Mathematics
- 2005

In this paper, we continue the development of a new combinatorial model for the irreducible characters of a complex semisimple Lie group. This model, which will be referred to as the alcove path… Expand

Grothendieck polynomials and the Yang - Baxter equation

- Mathematics
- 1994

A device and method is provided for the qualitative and semi-quantitative determination of the presence of phenothiazine-type drugs in urine. The article comprises an ion exchange resin which denotes… Expand