Quantum -determinant cyclic modules of
arXiv:math/0606123 · doi:10.1016/j.jalgebra.2006.12.015
Abstract
As a particular one parameter deformation of the quantum determinant, we introduce a quantum -determinant and study the -cyclic module generated by it: We show that the multiplicity of each irreducible representation in this cyclic module is determined by a certain polynomial called the -content discriminant. A part of the present result is a quantum counterpart for the result of Matsumoto and Wakayama (2005), however, a new distinguished feature arises in our situation.
27 pages, 1 figure