Refined canonical stable Grothendieck polynomials and their duals. I.(English)Zbl 1536.05462
Summary: In this paper we introduce refined canonical stable Grothendieck polynomials and their duals with two infinite sequences of parameters. These polynomials unify several generalizations of Grothendieck polynomials including canonical stable Grothendieck polynomials due toD. Yeliussizov [J. Algebr. Comb. 45, No. 1, 295–344 (2017;Zbl 1355.05263)], refined Grothendieck polynomials due toM. Chan andN. Pflueger [Algebr. Comb. 4, No. 1, 175–188 (2021;Zbl 1460.05193)], and refined dual Grothendieck polynomials due toP. Galashin et al. [Electron. J. Comb. 23, No. 3, Research Paper P3.14, 28 p. (2016;Zbl 1344.05148)]. We give Jacobi-Trudi-like formulas, combinatorial models, Schur expansions, Schur positivity, and dualities of these polynomials.
MSC:
| 05E05 | Symmetric functions and generalizations |
| 05E14 | Combinatorial aspects of algebraic geometry |
| 14M15 | Grassmannians, Schubert varieties, flag manifolds |
Cite
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