arXiv:1408.5708 Abstract | arXiv Analytics

arXiv:1408.5708 [math.RT]Abstract References Reviews Resources

Plethysm and lattice point counting

Published 2014-08-25Version 1

It is shown that the multiplicities in the plethysm of GL(n) are given by the answer to a lattice point counting problem. This problem is attacked with the help of computer algebra. An explicit answer is obtained for $S^\mu(S^k)$, when $\mu$ is any partition of 4 or 5. In the general case, asymptotics of the solution are studied.

Comments: 23 pages including appendix, 1 figure, computational results and code available at http://thomas-kahle.de/plethysm.html

Categories: math.RT, math.CO

Subjects: 20G05, 11P21, 11H06, 05A16, 52B20, 52B55, 20C15

Keywords: lattice point counting problem, explicit answer, computer algebra, general case, multiplicities

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