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Jun 23, 2017 at 17:41 comment added unknown it should be straight forward to automate finding such expressions : GAP for example can construct all these representations explicitly and can give decompositions of symmetric and exterior products..
Jun 23, 2017 at 14:22 history edited Robert Bryant CC BY-SA 3.0
Added a little more information
Jun 23, 2017 at 14:13 comment added Robert Bryant @SaalHardali: Yes, that was from memory. From time to time, I've had to use details of the representation theory of these two algebras in my work in differential geometry, and the above are some of the facts about them that I learned and have found useful again and again.
Jun 18, 2017 at 11:01 comment added Saal Hardali @Robert Bryant Was this from the top of your head? If not where can one find this kind of data. I know where to find tables which give dimensions and weights but this kind of data (i.e. using as much linear algebraic operations $\bigwedge^n, S^n$ decomposition of these etc...$ is much more helpful from a theoretical perspective. The only way I had success with aquiring such descriptions was by computing by myself small examples.
Mar 14, 2015 at 14:26 comment added Jjm Thank you very much, really. There is a big effort in your answer, and for sure it will be most helpful for me. Thanks!!
Mar 13, 2015 at 20:31 history edited Robert Bryant CC BY-SA 3.0
corrected some minor errors
Mar 12, 2015 at 12:44 history edited Robert Bryant CC BY-SA 3.0
added 49 characters in body
Mar 11, 2015 at 22:25 history answered Robert Bryant CC BY-SA 3.0