ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

7. Lie Groups and Lie Algebras

1991 MS Classification: 16, 17, 18 Phung, Ho Hai, Hanoi Institute of Mathematics, Vietnam Rational representations of matrix quantum groups of type A_{n} A matrix quantum group of type A_{n} is obtained from an even Hecke symmetry via Faddeev-Reshetikhin-Takhtajan’s construction. We study rational representations of these quantum groups. We show that the category rational representations of such a quantum group is uniquely determined, up to an equivalence of braided abelian categories, by the rank of the symmetry and a quantum parameter q. A notion of formal characters is also introduced. As a by-product, we derive a formula for computing irreducible characters of the Hecke algebras. Reference: Phung Ho Hai, On matrix quantum groups of type A_{n}, Preprint ICTP-97101, q-alg 9708007.