Representations of general linear groups and quantum groups

Abstract

The first part of this thesis studies the representations of general linear group GL(2,K) over a finite field K. For degree n extension Kn of K, we compute how an irreducible representation of GL(2,Kn) decomposes when it restricts on the sub group GL(2,K). The second part of the thesis studies the representations of quantum groups Uq(sl(n)). We classify all the irreducible representations of Uq(sl(2)) that contains a weight vector and we give a construction of an action of Uq(sl(n)) on the function spaces of n-variables using certain difference operators.

Date of Award	2001
Original language	English
Awarding Institution	The Hong Kong University of Science and Technology