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Bosonic Construction of Vertex Operator Para-Algebras from Symplectic Affine Kac-Moody Algebras
Michael David Weiner, Pennsylvania State University, Altoona, PA

Memoirs of the American Mathematical Society
1998; 106 pp; softcover
Volume: 135
ISBN-10: 0-8218-0866-4
ISBN-13: 978-0-8218-0866-5
List Price: US$49
Individual Members: US$29.40
Institutional Members: US$39.20
Order Code: MEMO/135/644
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Inspired by mathematical structures found by theoretical physicists and by the desire to understand the "monstrous moonshine" of the Monster group, Borcherds, Frenkel, Lepowsky, and Meurman introduced the definition of vertex operator algebra (VOA). An important part of the theory of VOAs concerns their modules and intertwining operators between modules. Feingold, Frenkel, and Ries defined a structure, called a vertex operator para-algebra (VOPA), where a VOA, its modules and their intertwining operators are unified.

In this work, for each \(n \geq 1\), the author uses the bosonic construction (from a Weyl algebra) of four level \(- 1/2\) irreducible representations of the symplectic affine Kac-Moody Lie algebra \(C_n^{(1)}\). They define intertwining operators so that the direct sum of the four modules forms a VOPA. This work includes the bosonic analog of the fermionic construction of a vertex operator superalgebra from the four level 1 irreducible modules of type \(D_n^{(1)}\) given by Feingold, Frenkel, and Ries. While they get only a VOPA when \(n = 4\) using classical triality, the techniques in this work apply to any \(n \geq 1\).


Graduate students, research mathematicians, and physicists working in representation theory and conformal field theory.

Table of Contents

  • Introduction
  • Bosonic construction of symplectic affine Kac-Moody algebras
  • Bosonic construction of symplectic vertex operator algebras and modules
  • Bosonic construction of vertex operator para-algebras
  • Appendix
  • Bibliography
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