Dimension formulas for some modular representations of the symplectic group in the natural characteristic
Representation Theory
2015-10-27 v2 Quantum Algebra
Abstract
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 This formula is equivalent to a special case of a formula contained in unpublished work of Foulle.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.
Keywords
Cite
@article{arxiv.1111.0240,
title = {Dimension formulas for some modular representations of the symplectic group in the natural characteristic},
author = {Patrick M. Gilmer and Gregor Masbaum},
journal= {arXiv preprint arXiv:1111.0240},
year = {2015}
}
Comments
7 pages; Added references to work of Foulle