Bosonic and Fermionic Realizations of The Affine Algebra sˆo_2n

Abstract

We give an explicit description of the Kac-Peterson-Lepowsky constr tion of the basic representation for the affine Lie algebra sˆo_2n(C). Using the conjugacy classes of the Weyl group of sˆo_2n(C), we describe all equivalent maximal Heisenberg subalgebras (HSA's) of the correspond: affine Lie algebra. We associate to these HSA's multicomponent charged and neutral free fermionic fields. The boson-fermion correspondence these fields provides us with fermionic vertex operators, whose 'norr, ordered products' give the (twisted) vertex operators of the Kac-Peters( Lepowsky construction.

Keywords:

• affine algebr
• fermionic fields
• Heisenbeg algebra
• kacmoody algebra
• kac-peterson-lepowsky construction
• vertex operator
• virasoro algebra
• weyl group

AMS classification::

• 17B65
• 17B67
• 22E65

^*Nieuwe Prinsengracht 77', 1018VR Amsterdam, The Netherlands. Part of this research was done while FtK was apost-doctoral fellow at the Faculteit Wiskunde en Informatica, Universiteit van Amsterdam.

^** [email protected] The research of J. van de Leur has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences. Part of this research was done while JvdL visited the Department of Mathematics of the University of Illinois at Urbana Champaign.

^*Nieuwe Prinsengracht 77', 1018VR Amsterdam, The Netherlands. Part of this research was done while FtK was apost-doctoral fellow at the Faculteit Wiskunde en Informatica, Universiteit van Amsterdam.

^** [email protected] The research of J. van de Leur has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences. Part of this research was done while JvdL visited the Department of Mathematics of the University of Illinois at Urbana Champaign.

Notes

^*Nieuwe Prinsengracht 77', 1018VR Amsterdam, The Netherlands. Part of this research was done while FtK was apost-doctoral fellow at the Faculteit Wiskunde en Informatica, Universiteit van Amsterdam.

^** [email protected] The research of J. van de Leur has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences. Part of this research was done while JvdL visited the Department of Mathematics of the University of Illinois at Urbana Champaign.

Additional information

Notes on contributors

Fons Ten Kroode

*

Johan Van De Leur

* *