2019/05/31 by Shinsuke Iwao · 2 citations
Mathematics · #math.CO #math.KT #msc:05E05 #msc:05A10
paper · pdf · doi:10.5802/alco.116
published as Algebraic Combinatorics, Volume 3 (2020) no. 5, pp. 1023-1040 · 19 pages
arxiv created 2020/04/08 · arxiv updated 2020/10/20
In this paper we study algebraic and combinatorial properties of Grothendieck polynomials and their dual polynomials by means of the Boson-Fermion correspondence. We show that these symmetric functions can be expressed as a vacuum expectation value of some operator that is written in terms of free-fermions. By using the free-fermionic expressions, we obtain alternative proofs of determinantal formulas and Pieri type formulas.