Two-Rowed Hecke Algebra Representations at Roots of Unity

Details Two-Rowed Hecke Algebra Representations at Roots of Unity Two-Rowed Hecke Algebra Representations at Roots of Unity

1995-09-07

arxiv.org/abs/q-alg/9509006v1

Mathematics

Quantum Algebra

LaTeX, 9 pages. Submitted for the Proceedings of the 4th International Colloquium ``Quantum Groups and Integrable Systems,'' P

Scientific paper

10.1007/BF01688823

In this paper, we initiate a study into the explicit construction of irreducible representations of the Hecke algebra $H_n(q)$ of type $A_{n-1}$ in the non-generic case where $q$ is a root of unity. The approach is via the Specht modules of $H_n(q)$ 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 $H_n(q)$-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.

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