A New Functor from E 6-mod to E 7-mod |
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| Authors: | Xiaoping Xu |
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| Institution: | 1. Hua Loo-Keng Key Mathematical Laboratory , Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences , Beijing , China xiaoping@math.ac.cn |
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| Abstract: | We find a new representation of the simple Lie algebra of type E 7 on the polynomial algebra in 27 variables. Using this representation and Shen's idea of mixed product, we construct a new functor from E 6-Mod to E 7-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 framework also gives a direct polynomial extension from irreducible E 6-modules to irreducible E 7-modules, which can be used to derive Gel'fand–Zetlin bases for E 7 from those for E 6 that can be obtained from those for D 5 according to our earlier work. |
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| Keywords: | Functor Irreducible module Polynomial extension Representation Simple Lie algebra |
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