A weak version of Kirillov's conjecture on Hecke–Grothendieck polynomials

Zhang，Zerui1,2; Chen，Yuqun1,2

2022-02-01

10.1016/j.jcta.2021.105555

JOURNAL OF COMBINATORIAL THEORY SERIES A   影响因子和分区

0097-3165

1096-0899

Hecke-Grothendieck polynomials were introduced by Kirillov as a common generalization of Schubert polynomials, dual α-Grothendieck polynomials, Di Francesco–Zinn–Justin polynomials, etc. Then Kirillov conjectured that the coefficients of every generalized Hecke-Grothendieck polynomial are nonnegative combinations of certain parameters. Here we prove a weak version of Kirillov's conjecture, that is, under certain conditions, every Hecke-Grothendieck polynomial has only nonnegative integer coefficients. In particular, the proof of this weak version of Kirillov's conjecture serves as a unified proof for the fact that all the Schubert polynomials, dual α-Grothendieck polynomials, and Di Francesco–Zinn–Justin polynomials have only nonnegative coefficients.

Gröbner–Shirshov basis Hecke-Grothendieck polynomial Positivity

SCI

英语

通讯

WOS:000710310600004

MATHEMATICS

2-s2.0-85117622060

Scopus

1.School of Mathematical Sciences,South China Normal University,Guangzhou,510631,China
2.International Center for Mathematics,SUSTech,Shenzhen,China

Zhang，Zerui,Chen，Yuqun. A weak version of Kirillov's conjecture on Hecke–Grothendieck polynomials[J]. JOURNAL OF COMBINATORIAL THEORY SERIES A,2022,186.

Zhang，Zerui,&Chen，Yuqun.(2022).A weak version of Kirillov's conjecture on Hecke–Grothendieck polynomials.JOURNAL OF COMBINATORIAL THEORY SERIES A,186.

Zhang，Zerui,et al."A weak version of Kirillov's conjecture on Hecke–Grothendieck polynomials".JOURNAL OF COMBINATORIAL THEORY SERIES A 186(2022).