A Conjecture on Hodge Integrals
Jian Zhou
TL;DR
This paper proposes a conjectural formula linking Hodge integrals with Kac-Moody algebra representation theory, extending previous conjectures and relevant to Gromov-Witten invariants calculations.
Contribution
It introduces a new conjectural formula connecting Hodge integrals to Kac-Moody algebra representations, generalizing prior conjectures.
Findings
Proposed a conjectural formula for generating series of Hodge integrals.
Connected Hodge integrals to representation theory of Kac-Moody algebras.
Presented examples illustrating the conjecture.
Abstract
We propose a conjectural formula expressing the generating series of some Hodge integrals in terms of representation theory of Kac-Moody algebras. Such generating series appear in calculations of Gromov-Witten invariants by localization techniques. It generalizes a formula conjectured by Mari\~no and Vafa, recently proved in joint work with Chiu-Chu Melissa Liu and Kefeng Liu. Some examples are presented.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Analytic Number Theory Research