Classification of finite irreducible modules over the Lie conformal superalgebra CK6

TL;DR

This paper classifies all finite degenerate irreducible modules over the exceptional Lie conformal superalgebra CK6, providing a comprehensive understanding of their structure and representation theory.

Contribution

It offers the first complete classification of finite degenerate irreducible modules over CK6, linking them to modules over the annihilation algebra E(1,6).

Findings

All continuous degenerate irreducible modules over E(1,6) are classified.

All finite degenerate irreducible modules over CK6 are classified.

The classification connects modules over CK6 with those over E(1,6).

Abstract

We classify all continuous degenerate irreducible modules over the exceptional linearly compact Lie superalgebra E(1, 6), and all finite degenerate irreducible modules over the exceptional Lie conformal superalgebra CK6, for which E(1, 6) is the annihilation algebra.