ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

7. Lie Groups and Lie Algebras

1991 MS Classification: 17, 05 Jing, Naihuan, North Carolina State University, USA Quantized Kac-Moody algebras and symmetric functions We introduce an affinization of the quantum Kac-Moody algebra associated to a symmetric generalized Cartan matrix. Based on the affinization, we construct a representation of the quantum Kac-Moody algebra by vertex operators from bosonic fields. The vertex representation gives an interesting and non-trivial combinatorial identity involving Hall-Littlewood polynomials. Ref: N. Jing, Quantum KAc-Moody algebras and vertex representations, Lett. Math. Phys., to appear. math. QA/9802036