Classification for $A_1\times A_1$

Arun Ram
Department of Mathematics and Statistics
University of Melbourne
Parkville, VIC 3010 Australia
aram@unimelb.edu.au

Last update: 31 March 2013

Classification for $A_1\times A_1$

The affine Hecke algebra of $A_1\times A_1$ is naturally isomorphic to $\stackrel{\sim }{H}{A}_1\otimes \stackrel{\sim }{H}{A}_1\text{.}$ The finite dimensional irreducible representations of $\stackrel{\sim }{H}{A}_1\otimes \stackrel{\sim }{H}{A}_1$ are all of the form $M\otimes N$ where $M$ and $N$ are finite dimensional irreducible representations of $\stackrel{\sim }{H}{A}_1\text{.}$

Notes and References

This is an excerpt of a preprint entitled Representations of rank two affine Hecke Algebras, written by Arun Ram, Department of Mathematics, Princeton University, August 5, 1989.

Research supported in part by National Science Foundation grant DMS-9622985, and a Postdoctoral Fellowship at Mathematical Sciences Research Institute.

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