Classification for ${A}_{1}×{A}_{1}$

Last update: 31 March 2013

Classification for ${A}_{1}×{A}_{1}$

The affine Hecke algebra of ${A}_{1}×{A}_{1}$ 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.