New York Journal of Mathematics
Volume 4 (1998) 223-235


David Joyner

A Correspondence for the Generalized Hecke Algebra of the Metaplectic Cover of SL(2,F), F p-adic

Published: October 22, 1998
Keywords: metaplectic groups, generalized Hecke algebras, representation theory, p-adic groups, SL(2)
Subject: 22E,11F

We prove, using a technique developed for GL(n) in Howe and Moy [H], a bijection between generalized Hecke algebras of G=SL(2,F) over a p-adic field and those of its n-fold metaplectic cover. This result implies that there is a canonical correspondence between irreducible admissible representations of G and genuine irreducible admissible representations of its metaplectic cover of "sufficiently large level" (depending on n,p).

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Mathematics Department, Chauvenet Hall, 572 Holloway Road, Annapolis, MD 21402, USA