Two-Rowed Hecke Algebra Representations at Roots of Unity
q-alg
2009-10-28 v1 Quantum Algebra
Abstract
In this paper, we initiate a study into the explicit construction of irreducible representations of the Hecke algebra of type in the non-generic case where is a root of unity. The approach is via the Specht modules of which are irreducible in the generic case, and possess a natural basis indexed by Young tableaux. The general framework in which the irreducible non-generic -modules are to be constructed is set up and, in particular, the full set of modules corresponding to two-part partitions is described. Plentiful examples are given.
Cite
@article{arxiv.q-alg/9509006,
title = {Two-Rowed Hecke Algebra Representations at Roots of Unity},
author = {T. A. Welsh},
journal= {arXiv preprint arXiv:q-alg/9509006},
year = {2009}
}
Comments
LaTeX, 9 pages. Submitted for the Proceedings of the 4th International Colloquium ``Quantum Groups and Integrable Systems,'' Prague, 22-24 June 1995