On the Kernel of the affine Dirac operator

Details On the Kernel of the affine Dirac operator On the Kernel of the affine Dirac operator

2008-04-22

arxiv.org/abs/0804.3495v3

Moscow Mathematical Journal, Vol. 8, n.4, 759--788 (2008)

Mathematics

Representation Theory

Comments: Latex file, 37 pages. This is a revised version of the paper published in Moscow Mathematical Journal, Vol. 8, n. 4,

Scientific paper

Let L be a finite-dimensional semisimple Lie algebra with a non-degenerate invariant bilinear form, \sigma an elliptic automorphism of L leaving the form invariant, and A a \sigma-invariant reductive subalgebra of L, such that the restriction of the form to A is non-degenerate. Consider the associated twisted affine Lie algebras L^, A^, and let F be the \sigma-twisted Clifford module over A^ associated to the orthocomplement of A in L. Under suitable hypotheses on\sigma and A, we provide a general formula for the decomposition of the kernel of the affine Dirac operator, acting on the tensor product of an integrable highest weight L^-module and F, into irreducible A^-submodules. As an application, we derive the decomposition of all level 1 integrable irreducible highest weight modules over orthogonal affine Lie algebras with respect to the affinization of the isotropy subalgebra of an arbitrary symmetric space.

Affiliated with

Also associated with

No associations

Rating

On the Kernel of the affine Dirac operator does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the Kernel of the affine Dirac operator, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the Kernel of the affine Dirac operator will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-675183