Cauchy identities for genus 2 Schur polynomials
S. Arthamonov, Sh. Shakirov, W. Yan

TL;DR
This paper introduces genus 2 Schur polynomials as a generalization of classical Schur functions, establishing Cauchy identities for these polynomials at the special case when parameters t and q equal 1.
Contribution
It develops a genus 2 analog of Cauchy identities specifically for Schur polynomials, extending the classical theory to a higher-genus setting.
Findings
Established Cauchy identities for genus 2 Schur polynomials at t=q=1
Connected the algebraic structure to genus 2 mapping class group actions
Extended classical symmetric function identities to higher genus context
Abstract
Genus 2 Macdonald polynomials generalize ordinary Macdonald polynomials in several aspects. First, they provide common eigenfunctions for commuting difference operators that generalize the Macdonald difference operators of type . Second, the algebra generated by these difference operators together with multiplication operators admits an action of genus 2 mapping class group (MCG) that generalizes the well-known action of for ordinary Macdonald polynomials. In this paper, one more important aspect of Macdonald theory is considered: the Cauchy identities. We construct a genus 2 generalization of Cauchy identities in the particular case when , i.e. for genus 2 Schur polynomials.
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