Compactification of classical groups

Classical vs. Landau-Ginzburg Geometry of Compactification

We consider superstring compactifications where both the classical description, in terms of a Calabi-Yau manifold, and also the quantum theory is known in terms of a Landau-Ginzburg orbifold model. In particular, we study (smooth) Calabi-Yau examples in which there are obstructions to parametrizing all of the complex structure cohomology by polynomial deformations thus requiring the analysis ba...

AFFINE SUBGROUPS OF THE CLASSICAL GROUPS AND THEIR CHARACTER DEGREES

In this paper we describe how the degrees of the irreducible characters of the affine subgroups of the classical groups under consideration can be found inductively. In [4] Gow obtained certain character degrees for all of the affine subgroups of the classical groups. We apply the method of Fischer to the above groups and, in addition to the character degrees given in [4], we obtain some ne...

Maximal prehomogeneous subspaces on classical groups

Suppose $G$ is a split connected‎ ‎reductive orthogonal or symplectic group over an infinite field‎ ‎$F,$ $P=MN$ is a maximal parabolic subgroup of $G,$ $frak{n}$ is‎ ‎the Lie algebra of the unipotent radical $N.$ Under the adjoint‎ ‎action of its stabilizer in $M,$ every maximal prehomogeneous‎ ‎subspaces of $frak{n}$ is determined‎.

Classical Groups

Limits of (certain) Cat(0) Groups, I: Compactification

The purpose of this paper is to investigate torsion-free groups which act properly and cocompactly on CAT(0) metric spaces which have isolated flats, as defined by Hruska [18]. Our approach is to seek results analogous to those of Sela, Kharlampovich and Miasnikov for free groups and to those of Sela (and Rips and Sela) for torsion-free hyperbolic groups. This paper is the first in a series. In...