Abelian subalgebras in Z2-graded lie algebras; partitions, young diagrams and ballot numbers.

摘要

The dissertation is broken into two parts. Part I deals with the following problem: suppose g=g0⊕g1 is a simple Z2 -graded Lie algebra and let b0 be a fixed Borel subalgebra of g0 ; describe and enumerate the abelian b0 -stable subalgebras of g1 . The original proof uses a geometric approach; in Part I, we utilize an algebraic method which better describes the corresponding subalgebras. Part II focuses on a generalization of a combinatorial problem related to the representation theory of affine Lie algebras; given an arbitrary partition, we describe an iterative algorithm which at every level generates a ballot number of partitions.