Bosonic Construction of Vertex Operator Par-Algebars from Symplectic Affine Kac-Moody Algebras (Memoirs of the AMS) (Memoirs of the American Mathematical Society) - Softcover

Weiner, Michael David

Softcover

ISBN 10: 0821808664 ISBN 13: 9780821808665

Publisher: American Mathematical Society, 1999

Synopsis

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 $n \geq 1$.

Edition details

• Publisher: American Mathematical Society
• Publication date: 1999
• Language: English
• ISBN 10: 0821808664
• ISBN 13: 9780821808665
• Binding: Paperback
• Number of pages: 106