Grobner-shirshov bases for repressentations of lie algebras and hecke algebras of type A

摘要

In this paper we discuss the Grobner-Shirshov basis theory for representations of Lie algebras and Hecke algebras of type A. We describe Grobner-Sliirshov pairs and monomial bases for the Weyl modules over the special linear Lie algebras, and present the structure of the Specht modules over the Hecke algebras through Grobner-Shirshov pairs and monomial bases.