2025/08/20 by Shinsuke Iwao, Iwao, Shinsuke
Mathematics · #05E05 #14M15 #19L47 #Advanced Topics in Algebra #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #K-Theory and Homology (math.KT) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2508.14484
openalex publication_date 2025/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper presents an elementary introduction on K-theoretic Q-functions, which were introduced by Ikeda and Naruse in 2013. These functions, which serve as K-theoretic analogs of Schur Q-functions, are known to possess combinatorial and algebraic constructions. In a 2022 paper, the author introduced ``β-deformed power-sums" to provide a simpler, more algebraic construction of these functions. Since the original approach relies on fermionic operators and vacuum expectation values, this paper presents a more accessible, purely algebraic treatment, following the exposition of Schur Q-functions in Macdonald's standard textbook. We also show that the algebra of dual Q-cancellation property with integer coefficients is generated by dual K-Q-functions associated with an odd row partition.