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1. CJM Online first

Szpruch, Dani
 Symmetric Genuine Spherical Whittaker Functions on $\overline{GSp_{2n}(F)}$ Let $F$ be a p-adic field of odd residual characteristic. Let $\overline{GSp_{2n}(F)}$ and $\overline{Sp_{2n}(F)}$ be the metaplectic double covers of the general symplectic group and the symplectic group attached to the $2n$ dimensional symplectic space over $F$. Let $\sigma$ be a genuine, possibly reducible, unramified principal series representation of $\overline{GSp_{2n}(F)}$. In these notes we give an explicit formulas for a spanning set for the space of Spherical Whittaker functions attached to $\sigma$. For odd $n$, and generically for even $n$, this spanning set is a basis. The significant property of this set is that each of its elements is unchanged under the action of the Weyl group of $\overline{Sp_{2n}(F)}$. If $n$ is odd then each element in the set has an equivariant property that generalizes a uniqueness result of Gelbart, Howe and Piatetski-Shapiro. Using this symmetric set, we construct a family of reducible genuine unramified principal series representations which have more then one generic constituent. This family contains all the reducible genuine unramified principal series representations induced from a unitary data and exists only for $n$ even. Keywords:metaplectic group, Casselman Shalika FormulaCategory:11F85

2. CJM 2012 (vol 64 pp. 497)

Li, Wen-Wei
 Le lemme fondamental pondÃ©rÃ© pour le groupe mÃ©taplectique Dans cet article, on Ã©nonce une variante du lemme fondamental pondÃ©rÃ© d'Arthur pour le groupe mÃ©taplectique de Weil, qui sera un ingrÃ©dient indispensable de la stabilisation de la formule des traces. Pour un corps de caractÃ©ristique rÃ©siduelle suffisamment grande, on en donne une dÃ©monstration Ã  l'aide de la mÃ©thode de descente, qui est conditionnelle: on admet le lemme fondamental pondÃ©rÃ© non standard sur les algÃ¨bres de Lie. Vu les travaux de Chaudouard et Laumon, on s'attend Ã  ce que cette condition soit ultÃ©rieurement vÃ©rifiÃ©e. Keywords:fundamental lemma, metaplectic group, endoscopy, trace formulaCategories:11F70, 11F27, 22E50

3. CJM 2011 (vol 64 pp. 669)

Pantano, Alessandra; Paul, Annegret; Salamanca-Riba, Susana A.
 The Genuine Omega-regular Unitary Dual of the Metaplectic Group We classify all genuine unitary representations of the metaplectic group whose infinitesimal character is real and at least as regular as that of the oscillator representation. In a previous paper we exhibited a certain family of representations satisfying these conditions, obtained by cohomological induction from the tensor product of a one-dimensional representation and an oscillator representation. Our main theorem asserts that this family exhausts the genuine omega-regular unitary dual of the metaplectic group. Keywords:Metaplectic group, oscillator representation, bottom layer map, cohomological induction, Parthasarathy's Dirac Operator Inequality, pseudospherical principal seriesCategory:22E46