A normal subgroup of a semisimple Lie group is closed

The topology of a semisimple Lie group is essentially unique

We study locally compact group topologies on simple and semisimple Lie groups. We show that the Lie group topology on such a group S is very rigid: every “abstract” isomorphism between S and a locally compact and σ -compact group Γ is automatically a homeomorphism, provided that S is absolutely simple. If S is complex, then noncontinuous field automorphisms of the complex numbers have to be con...

Characterizing the Multiplicative Group of a Real Closed Field in Terms of its Divisible Maximal Subgroup

Subgroup growth of lattices in semisimple Lie groups

Proving a conjecture posed in [5], we give very precise bounds for the congruence subgroup growth of arithmetic groups. This allows us to determine the subgroup growth of irreducible lattices of semisimple Lie groups. In the most general case our results depend on the Generalized Riemann Hypothesis for number fields but we can state the following unconditional theorem: Let G be a simple Lie gro...

Picard–lefschetz Theory and Characters of a Semisimple Lie Group

The paper applies Picard-Lefschetz theory to the distribution characters of infinite dimensional representations of semisimple Lie groups and analyzes their asymptotic behavour at the identity.

On the Characters of a Semisimple Lie Group

where dx is the Haar measure of G and C?(G) is the set of all (complexvalued) functions on G which are everywhere indefinitely differentia t e and which vanish outside a compact set. V is called the Gârding subspace of § . Let R and C be the fields of real and complex numbers respectively and g0 the Lie algebra of G. We complexify g0 to Q and denote by $8 the universal enveloping algebra of Q [...