A New Factor from E6-Mod to E7-Mod

Details A New Factor from E6-Mod to E7-Mod A New Factor from E6-Mod to E7-Mod

2012-01-26

arxiv.org/abs/1201.5473v1

Mathematics

Representation Theory

45pages

Scientific paper

We find a new representation of the simple Lie algebra of type $E_7$ on the polynomial algebra in 27 variables, which gives a fractional representation of the corresponding Lie group on 27-dimensional space. Using this representation and Shen's idea of mixed product, we construct a functor from $E_6$-{\bf Mod} to $E_7$-{\bf Mod}. A condition for the functor to map a finite-dimensional irreducible $E_6$-module to an infinite-dimensional irreducible $E_7$-module is obtained. Our general frame also gives a direct polynomial extension from irreducible $E_6$-modules to irreducible $E_7$-modules. The obtained infinite-dimensional irreducible $E_7$-modules are $({\cal G},K)$-modules in terms of Lie group representations. The results could be used in studying the quantum field theory with $E_7$ symmetry and symmetry of partial differential equations.

Affiliated with

Also associated with

No associations

Rating

A New Factor from E6-Mod to E7-Mod 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 A New Factor from E6-Mod to E7-Mod, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A New Factor from E6-Mod to E7-Mod will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-445275