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arXiv · 2508.14484

An elementary construction of the ring of dual $K$-$Q$-cancellation property

Shinsuke Iwao
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Abstract

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.

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Shinsuke Iwao. 2025-08-20. An elementary construction of the ring of dual $K$-$Q$-cancellation property. https://arxiv.org/abs/2508.14484

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