Jordan blocks of unipotent elements in some irreducible representations of classical groups in good characteristic

Korhonen, Mikko Tapani2019-07-082019-07-082019-07-082019-06-1910.1090/proc/14570https://infoscience.epfl.ch/handle/20.500.14299/158932Let $ G$ be a classical group with natural module $ V$ over an algebraically closed field of good characteristic. For every unipotent element $ u$ of $ G$, we describe the Jordan block sizes of $ u$ on the irreducible $ G$-modules which occur as composition factors of $ V \otimes V^*$, $ \wedge ^2(V)$, and $ S^2(V)$. Our description is given in terms of the Jordan block sizes of the tensor square, exterior square, and the symmetric square of $ u$, for which recursive formulae are known.Jordan blocks of unipotent elements in some irreducible representations of classical groups in good characteristictext::journal::journal article::research article