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By W. W. Sawyer

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For centuries, the learn of elliptic curves has performed a relevant position in arithmetic. The previous century particularly has noticeable large growth during this examine, from Mordell's theorem in 1922 to the paintings of Wiles and Taylor-Wiles in 1994. still, there stay many primary questions the place we don't even recognize what kind of solutions to count on.

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1 Remark. L* jd*.

Thus we recover the following result, which may also be seen by inspection of the usual formulas for the Schrodinger representation as a representation on £2(1R). 10 Remark. The Schrodinger-Weil representation ir~w is unitarizable. e. 2. Models for infinitesimal representations and unitarizability 47 For 7l-ta we come up with II WI+211 2 = l+2( -2- ko l+2 ) 2 + -2-1 IlwI11 and for ir ko with IIW-C/+2) II 2 = l+2( -2- ko l+2 + -2- ) - 1 Ilw-III 2 showing that in both cases we have to require ko gives the following result.

Summarizing we obtain the following result. 1 Theorem. The above construction gives a 1-1 correspondence between the irreducible unitary projective representations ofSL(2, R) with multiplier>.. and the irreducible unitary representations of G J (R) with non-trivial central character 'ljJm. The corresponding non-archimedean result is as follows . 2 Theorem. Let F be a p-adic field. There is a 1-1 correspondence between the irreducible smooth projective representations ofSL(2, F) with multiplier>..

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A Concrete Approach to Abstract Algebra by W. W. Sawyer


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