Frontiers of Mathematics in China >

2015 , Vol. 10 >Issue 5: 1041 - 1056

DOI: https://doi.org/10.1007/s11464-015-0471-1

RESEARCH ARTICLE

A fundamental representation of quantum generalized Kac-Moody algebras with one imaginary simple root

  • Jiangrong CHEN 1 ,
  • Zhonghua ZHAO , 2
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  • 1. School of Statistics, Capital University of Economics and Business, Beijing 100070, China
  • 2. Department of Mathematics and Computer Science, School of Science, Beijing University of Chemical Technology, Beijing 100029, China

Received date: 19 Dec 2013

Accepted date: 09 Apr 2015

Published date: 24 Jun 2015

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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Abstract

We consider the Borcherds-Cartan matrix obtained from a symmetrizable generalized Cartan matrix by adding one imaginary simple root. We extend the result of Gebert and Teschner [Lett. Math. Phys., 1994, 31: 327-334] to the quantum case. Moreover, we give a connection between the irreducible dominant representations of quantum Kac-Moody algebras and those of quantum generalized Kac-Moody algebras. As the result, a large class of irreducible dominant representations of quantum generalized Kac-Moody algebras were obtained from representations of quantum Kac-Moody algebras through tensor algebras.

Key words： Quantum generalized Kac-Moody algebra; tensor algebra; fundamental representation

Cite this article

Jiangrong CHEN , Zhonghua ZHAO . A fundamental representation of quantum generalized Kac-Moody algebras with one imaginary simple root[J]. Frontiers of Mathematics in China, 2015 , 10(5) : 1041 -1056 . DOI: 10.1007/s11464-015-0471-1

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