Mathematics – Representation Theory
Scientific paper
2005-12-14
Mathematics
Representation Theory
23 pages, 2 figures
Scientific paper
Let K be an algebraically closed field of characteristic p>0 and let Sp(2m) be the symplectic group of rank m over K. The main theorem of this article gives the character of the rational simple Sp(2m)-modules with fundamental highest weight as an explicit alternating sum of characters of Weyl modules. One obtains several formulae for the dimensions of these simple modules, what allows us to investigate the asymptotic behavior of these dimensions, for a given p, when the rank m is growing towards infinity. One also gets the simple Weyl modules with fundamental highest weight, and the article ends with an application to the modular representation theory of the symmetric group.
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