## 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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