Abstract
This paper gives a complete analysis of the irreducible representations of affine Hecke algebras of rank two when the parameter q is not a root of unity. The irreducible representations are classified in terms of the Kazhdan-Lusztig classification and the relation to the Springer correspondence is given in detail. Each irreducible representation is constructed explicitly. These results are used in a crucial way in the classification of calibrated representations of general affine Hecke algebras as done in [Ra1] and [Ra4]. Though the same methods can be used to handle the very few root of unity cases (q2k = 1, k = 0, 1, 2, and also k = 3 in type A2, k = 4 in type B2 and k = 3,6 in type G2) which have different representations, this extra analysis is not completed in this paper.
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© 2003 Hindustan Book Agency
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Ram, A. (2003). Representations of Rank Two Affine Hecke Algebras. In: Musili, C. (eds) Advances in Algebra and Geometry. Hindustan Book Agency, Gurgaon. https://doi.org/10.1007/978-93-86279-12-5_6
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DOI: https://doi.org/10.1007/978-93-86279-12-5_6
Publisher Name: Hindustan Book Agency, Gurgaon
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