2023/01/30 by Iwao, Shinsuke · 1 citation
#05E05 #05E14 #13M10 #14N15 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #K-Theory and Homology (math.KT)
paper · doi:10.48550/arxiv.2301.12741
In this paper, we present a new algebraic description of Ikeda-Naruse's K-theoretic Schur P- and Q-functions and their dual functions in terms of neutral fermion operators. We introduce four families of ``β-deformed neutral-fermion operators'' depending on a parameter β, which reduce to the usual neutral-fermion operators when β is zero. Using these operators, we introduce two families of β-deformed vertex operators, power sums, and boson-fermion correspondences. From commutation relations among these operators, we naturally derive the K-theoretic Cauchy kernel of Nakagawa-Naruse. Exploiting this fact, we show that the four K-theoretic functions can be realized as vacuum expectation values of certain β-deformed fermionic operators. This presentation also allows us to derive generating functions for the dual K-theoretic P-and Q-functions, as conjectured by Nakagawa-Naruse.