Characters of the irreducible representations with fundamental highest weight for the symplectic group in characteristic p

Sebastien Foulle

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arxiv math/0512312 v1 pith:LPLCBKMZ submitted 2005-12-14 math.RT

Characters of the irreducible representations with fundamental highest weight for the symplectic group in characteristic p

Sebastien Foulle This is my paper

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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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On a symplectic quantum Howe duality
math.RT 2023-03 unverdicted novelty 7.0

Proves nonsemisimple quantum Howe duality for Sp(2n) and SL(2) on exterior algebra of type C, with character formulas and canonical bases.