arXiv subjects

Uwe Weselmann

Publications and source records attributed to Uwe Weselmann.

2 recordsLinked to original sources

arXiv2013

Siegel Modular Varieties and the Eisenstein Cohomology of $\PGL_{2g+1}$

We use the twisted topological trace formula developed in an earlier paper to understand liftings from symplectic to general linear groups. We analyse the lift from $\SP_{2g}$ to $\PGL_{2g+1}$ over the ground field $\Q$ in further detail, and we get a description of the image of this lift for the $L^2$ cohomology of $\SP_{2g}$ (which is related to the intersection cohomology of the Shimura variety attached to $\GSp_{2g}$) in terms of the Eisenstein cohomology of the general linear group, whose building constituents are cuspidal representations of Levi groups. This description may be used to understand endoscopic and CAP-representations of the symplectic group.

math.RT↗

arXiv2013

Remarks on the Fundamental Lemma for stable twisted Endoscopy of Classical Groups

The twisted fundamental lemmas for three series of stable twisted endoscopy (Sp_{2n} to PGL_{2n+1}, GSpin_{2n+1} to GL_{2n}\times GL_1, Sp_{2n} to SO_{2n+2}) will be reduced to a fundamental-lemma-like statement for ordinary (i.e. untwisted) stable orbital integrals on the groups $\SO_{2n+1}$ of type $B_n$ resp. $\SP_{2n}$ of type $C_n$. This manusript, written around 2001, anticipates similar results of Waldspurger (2008), and may be used to reduce the twisted fundamental lemma to the work of Ngo. The original aim was to reduce the fundumantal lemma for the lift from Sp_4 to PGL_5 to the twisted fundamental lemma for the lift from GSp_4=GSpin_5 to Gl_4 \times GL_1.

math.RT↗