Abstract

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Often an algebra admits some interesting deformations. For instances, Hecke 

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algebras of Coxeter groups are deformation of  group algebras of Coxeter groups,

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quantized enveloping algebras are deformation of universal enveloping algebras 

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of Lie algebras. A natural question is whether a deformation B of  an algebra A 

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is isomorphic to the orginal algebra A. When a Coxeter group is a Weyl group 

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(symmetric group is a Weyl group), In 1964 Iwahori conjectured that the Hecke 

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algebras of a Weyl group is isomorphic to the group algebra of the Weyl group. 

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This conjecture  was proved later by Tits, Lusztig, Gyoja. It is natural to 

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consider Iwahori's problem for other Coxeter groups. We will show that Iwahor's 

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problem for affine Weyl group has a negative answer. This is a joint work with 

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T. Shoji.