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Calculus of twisted vertex operators.

J Lepowsky1

  • 1Department of Mathematics, Rutgers University, New Brunswick, NJ 08903.

Proceedings of the National Academy of Sciences of the United States of America
|December 1, 1985
PubMed
Summary

Researchers introduce twisted and shifted vertex operators derived from arbitrary even lattices. This novel approach yields realizations of twisted affine Lie algebras, generalizing existing constructions through a unique calculus.

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Area of Science:

  • Algebraic Geometry
  • Mathematical Physics
  • Representation Theory

Background:

  • Vertex operators and Lie algebras are fundamental in theoretical physics and mathematics.
  • Existing constructions of affine Lie algebras often rely on specific lattice types.

Purpose of the Study:

  • To introduce a generalized method for constructing twisted affine Lie algebras.
  • To explore the properties of twisted and shifted vertex operators.
  • To establish a self-contained calculus for these operators.

Main Methods:

  • Starting with an arbitrary isometry of an even lattice.
  • Introducing twisted and shifted vertex operators.
  • Analyzing the commutation relations of these operators.

Main Results:

  • Demonstrated that commutators of these operators realize twisted affine Lie algebras.
  • Showcased a construction that generalizes several known methods.
  • Developed a self-contained calculus for the introduced operators.

Conclusions:

  • The introduced vertex operators offer a unified framework for realizing twisted affine Lie algebras.
  • The developed calculus provides a powerful tool for further research in related areas.
  • This work expands the understanding of algebraic structures in mathematical physics.

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