What question did this study set out to answer?

The aim is to develop a new method for constructing irreducible modules for toroidal sl2.

March 28, 2026

A new construction of irreducible quasi-finite highest weight modules for toroidal 𝔰𝔩 2

Key Points

The aim is to develop a new method for constructing irreducible modules for toroidal sl2.
Developed a new free field-like construction method for modules.
Analyzed the irreducibility of certain Verma modules.
Investigated the characteristics of weight spaces associated with the modules.
Demonstrated a new class of irreducible modules exists for toroidal sl2.
Established criteria for the irreducibility of specific Verma modules.
Showed weight spaces of the modules are finite-dimensional.

Abstract

In this paper, we present a new free field(-like) construction of irreducible modules for toroidal 𝔰𝔩 2 with finite dimensional weight spaces and trivial central action. To this end, we also determine the irreducibility of certain Verma modules for generalized Takiff algebras associated to 𝔰𝔩 2 .

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Cite This Study

Feng et al. (Thu,) studied this question.

synapsesocial.com/papers/69c772818bbfbc51511e3019 https://doi.org/https://doi.org/10.1142/s0219498826400037

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