Hecke algebras and quantum general linear groups (Q1380138)

The author constructs the Hecke algebra of the symmetric group from the quantum general linear group. Then he obtains certain representations of the Hecke algebra, which are essentially isomorphic to the Specht modules, using polynomial representations of quantum groups. As a consequence, he derives the quantum Plücker relations given by \textit{E. J. Taft} and \textit{J. Towber} [J. Algebra 142, 1-36 (1991; Zbl 0739.17007)]. A sequel is promised on further relations between Hecke algebras and quantum general linear groups.