Comparisons of General Linear Groups and their Metaplectic Coverings I

Abstract

Abstract. We prepare for a comparison of global trace formulas of general linear groups and their metaplectic coverings. In particular, we generalize the local metaplectic correspondence of Flicker and Kazhdan and describe the terms expected to appear in the invariant trace formulas of the above covering groups. The conjectural trace formulas are then placed into a form suitable for comparison.

Preparation and characterization of photoreactive derivatives of GnRH

“…Following photoaffinity 434 labeling of cells with the photoreactive peptide and removal of noncovalently bound molecules, a potent competitive inhibitory GnRH analog was added to the incubation medium in different concentrations. This analog is known completely to inhibit lo-' M GnRH induced LH release at concentrations of M (20). As shown in Table 1, even M inhibitor did not significantly decrease LH release induced by [D-Lys(NAPS)] GnRH-EA covalently attached to the cells by photolysis.…”

Metaplectic tensor products for irreducible representations

“…In this equation, and for the duration of this paper, 0 ≤ c ≤ n − 1 is a fixed integer. This equation determines (an isomorphism class of) an n-fold metaplectic covering group GL(r, F ) as defined in any of [8], [4] or [10].…”

“…This allows us to form the unique parabolically induced representation ind G P (⊗ρ i ) as in Proposition 26.2 [4]. This has consequences for several metaplectic correspondences: The local correspondence of §27.3 [4] holds for all coverings (Appendix [3]); the assumption on the local correspondence of p. 99 [10] may be removed; and the global correspondence of [11] holds in more generality. (To be precise, Assumption 1 [11] may be weakened to the assumption that n is relatively prime to r!…”

La formule des traces pour les revêtements de groupes réductifs connexes. I. Le développement géométrique fin

“…Malheureusement ils ne considèrent pas les autres revêtements. De plus, vu la profondeur des travaux d'Arthur sur la formule des traces invariante [6,7], les justifications données dans [25] ne sont peut-être pas suffisantes.…”