1202.1935 (Jan Troost)

Models for Modules    [PDF]

Jan Troost

We recall the structure of the indecomposable sl(2) modules in the
Bernstein-Gelfand-Gelfand category O. We show that all these modules can arise
as quantized phase spaces of physical models. In particular, we demonstrate in
a path integral discretization how a redefined action of the sl(2) algebra over
the complex numbers can glue finite dimensional and infinite dimensional
highest weight representations into indecomposable wholes. Furthermore, we
discuss how projective cover representations arise in the tensor product of
finite dimensional and Verma modules and give explicit tensor product
decomposition rules. The tensor product spaces can be realized in terms of
product path integrals. Finally, we discuss relations of our results to brane
quantization and cohomological calculations in string theory.

View original: http://arxiv.org/abs/1202.1935