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Affine Hecke Algebras, Cyclotomic Hecke algebras and Clifford Theory

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Book cover A Tribute to C. S. Seshadri

Abstract

We show that the Young tableaux theory and constructions of the irreducible representations of the Weyl groups of type A, B and D, Iwahori-Hecke algebras of types A, B, and D, the complex reflection groups G(r,p,n) and the corresponding cyclotomic Hecke algebras Hr,p,n, can be obtained, in all cases, from the affine Hecke algebra of type A. The Young tableaux theory was extended to affine Hecke algebras (of general Lie type) in recent work of A. Ram. We also show how (in general Lie type) the representations of general affine Hecke algebras can be constructed from the representations of simply connected affine Hecke algebras by using an extended form of Clifford theory. This extension of Clifford theory is given in the Appendix.

Dedicated to Professor C.S. Seshadri on the occasion of his 70th birthday

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Wisconsin-Madison, Madison, WI, 53706, USA

    Arun Ram

  2. Department of Mathematics, NSW, 2308, Australia

    Jacqui Ramagge

  3. University of Newcastle, NSW, 2308, Australia

    Jacqui Ramagge

Authors
  1. Arun Ram
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  2. Jacqui Ramagge
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Editor information

V. Lakshmibai V. Balaji V. B. Mehta K. R. Nagarajan K. Pranjape P. Sankaran R. Sridharan

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© 2003 Hindustan Book Agency

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Ram, A., Ramagge, J. (2003). Affine Hecke Algebras, Cyclotomic Hecke algebras and Clifford Theory. In: Lakshmibai, V., et al. A Tribute to C. S. Seshadri. Hindustan Book Agency, Gurgaon. https://doi.org/10.1007/978-93-86279-11-8_26

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