Location of Repository

Let $F$ be a field of characteristic $p$. We show that $\Hom_{F\Sigma_n}(S^\lambda, S^\mu)$ can have arbitrarily large dimension as $n$ and $p$ grow, where $S^\lambda$ and $S^\mu$ are Specht modules for the symmetric group $\Sigma_n$. Similar results hold for the Weyl modules of the general linear group. Every previously computed example has been at most one-dimensional, with the exception of Specht modules over a field of characteristic two. The proof uses the work of Chuang and Tan, providing detailed information about the radical series of Weyl modules in Rouquier blocks

Topics:
Mathematics - Representation Theory, 20C20

Year: 2011

OAI identifier:
oai:arXiv.org:1103.0246

Provided by:
arXiv.org e-Print Archive

Download PDF:To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.