Integrable Representations for Equivariant Map Algebras Associated with Borel-de Siebenthal Pairs
- Author(s): O'Dell, Matthew Tyler
- Advisor(s): Chari, Vyjayanthi
- et al.
Borel and de-Siebenthal classified the maximal connected subgroups of maximal rank
of a connected compact Lie group. This result can be rephrased in terms of automorphisms of the
semisimple Lie algebra and the subalgebra of fixed points. They also give rise in a natural way
to a maximal parabolic subalgebra of an affine Lie algebra. In the case when the automorphism
is non-trivial, we shall see that the parabolic subalgebra is isomorphic to an equivariant map
We develop the theory of integrable representations of such Lie algebras. In particular, we
define and study global Weyl modules. These are closely related to the module category of a
commutative associative algebra. In this dissertation, we give a presentation of this algebra, and give
partial results toward a dimension formula for local Weyl modules.