Mathematical Research Letters

Volume 19 (2012)

Number 2

Shimura correspondence for finite groups

Pages: 461 – 468

DOI: http://dx.doi.org/10.4310/MRL.2012.v19.n2.a16

Author

Gordan Savin (Department of Mathematics, University of Utah, Salt Lake City, UT 84112, U.S.A.)

Abstract

Let $\bbQ_{2^{s}}$ be the unique unramifed extension of thetwo-adic field $\bbQ_{2}$ of the degree $s$. Let $R$ be thering of integers in $\bbQ_{2^{s}}$ Let $G$ be a simplyconnected Chevalley group corresponding to an irreduciblesimply laced root system. Then the finite group $G(R/4R)$has a two-fold central extension $G'(R/4R)$ constructed bymeans of the Hilbert symbol on $\bbQ_{2^{s}}$. In thispaper, we construct a natural correspondence betweengenuine representations of $G'(R/4R)$ and representationsof the Chevalley group $G(R/2R)$.

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