TL;DR
This paper explores the relationship between rational versions of symmetric function operators and bases, extending the classical Pieri rule using elliptic Hall algebra and stable basis constructions.
Contribution
It introduces a rational generalization of the Pieri rule connecting elliptic Hall algebra operators with Maulik-Okounkov stable bases.
Findings
Established a link between rational operators and stable bases
Extended Pieri rule to rational parameters
Provided new algebraic identities involving elliptic Hall algebra
Abstract
The Pieri rule is an important theorem which explains how the operators e_k of multiplication by elementary symmetric functions act in the basis of Schur functions s_lambda. In this paper, for any rational number m/n, we study the relationship between the rational version e_k^{m/n} of the operators (given by the elliptic Hall algebra) and the "rational" version s_lambda^{m/n} of the basis (given by the Maulik-Okounkov stable basis construction)
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Taxonomy
TopicsLaw, logistics, and international trade