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  • 3214290.PDF.jpg
  • Thesis

  • Authors: Golsefidy, Alireza Salehi (2006)

  • We will show that G(IFq[t]) is a lattice of minimum covolume among the lattices in G(Tq((t-1))), if G is a simply connected classical Chevalley group and p > 7. This is analogous to the Lubotzky's result [Lu90] for the case of SIL2. Moreover, we will show that up to an automorphism of G(IFq((t-1))), lattice of minimum covolume is unique. Along the way, we would prove a quantitative version of a theorem by Kazhdan and Margulis. Namely we prove that any lattice in G = G(IFq((t-1))) can be pushed out of the 1" congruence subgroup by applying an adjoint automorphism of G, where l is the maximum coefficient appearing in the highest root of G.

  • 3214249.PDF.jpg
  • Thesis

  • Authors: Mallahi-Karai, Keivan (2006)

  • In this thesis we study two different aspects of certain classes of arithmetic groups. In the first chapter, we prove a classification for the relative growth type of lattices in higher rank algebraic groups. It states that the growth of number of points in the intersection of balls with arbitrary subgroups of lattices in higher rank algebraic groups is either polynomial or exponential. This generalizes a theorem of Lubotzky, Mozes, and Raghunathan who proved the same statement for cyclic subgroups. The second part of the thesis proposes a method for finding a lower bound for the Kazhdan constants for the tame automorphisms of the free nilpotent groups. Such groups arise very natural...

  • 3214206.PDF.jpg
  • Thesis

  • Authors: Duncan, John Francis Robert (2006)

  • We introduce the notion of super vertex operator algebra with enhanced conformal structure, which is a refinement of the notion of super vertex operator algebra, and we present applications of this notion to three sporadic simple groups: the largest sporadic group of Conway, the sporadic group of Suzuki, and the sporadic group of Rudvalis. For the Conway group we construct what may be considered a natural super-analogue of the Moonshine Module, where the role of the Virasoro algebra is now played by the N = 1 Virasoro superalgebra, and we find that the full group of automorphisms is Conway's largest sporadic group. We also verify a uniqueness result for this object, which is directly...