Abstract
In this paper, we initiate a study into the explicit construction of irreducible representations of the Hecke algebraH n (q) of typeA n-1 in the non-generic case whereq is a root of unity. The approach is via the Specht modules ofH 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-genericH 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.
Similar content being viewed by others
References
Dipper R. and James G.D.: Proc. London Math. Soc.52 (1986) 20.
Wenzl H.: Invent. Math.92 (1988) 349.
James G.D. and Kerber A.: The Representation Theory of the Symmetric Group, Addison-Wesley, Reading (MA), 1981.
King R.C. and Wybourne B.G.: J. Phys. A: Math. Gen.23 (1990) L1193.
King R.C. and Wybourne B.G.: J. Math. Phys.33 (1992) 4.
Gyoja A.: Osaka J. Math.23 (1986) 841.
Burdík Č., King R.C, and Welsh T.A.: Int. J. Mod. Phys. B (to appear in 1995).
James G.D.: Proc. London Math. Soc.60 (1990) 225.
Cummins C.J. and King R.C.: J. Phys. A: Math. Gen.25 (1992) L789.
Dipper R. and James G.D.: Proc. London Math. Soc.54 (1987) 57.
Ram A.: Invent. Math.106 (1991) 461.
Van der Jeugt J.: J. Phys. A: Math. Gen.24 (1991) 3719.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Welsh, T.A. Two-rowed Hecke algebra representations at roots of unity. Czech J Phys 46, 283–291 (1996). https://doi.org/10.1007/BF01688823
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01688823