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arxiv 1111.0240 v2 pith:GJ3YTL4R submitted 2011-11-01 math.RT math.QA

Dimension formulas for some modular representations of the symplectic group in the natural characteristic

Patrick M. Gilmer , Gregor Masbaum This is my paper
classification math.RT math.QA
keywords formuladimensionsproofrepresentationscharacteristicfieldfoulleirreducible
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We compare the dimensions of the irreducible Sp(2g,K)-modules over a field K of characteristic p constructed by Gow with the dimensions of the irreducible Sp(2g,F_p)-modules that appear in the first approximation to representations of mapping class groups of surfaces in Integral Topological Quantum Field Theory. For this purpose, we derive a trigonometric formula for the dimensions of Gow's representations. This formula is equivalent to a special case of a formula contained in unpublished work of Foulle. Our direct proof is simpler than the proof of Foulle's more general result, and is modeled on the proof of the Verlinde formula in TQFT.

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  1. 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.