Prehomogeneous spaces for Borel subgroups of general linear groups
| dc.creator | Goodwin, Simon M. | |
| dc.creator | Hille, Lutz | |
| dc.date | 2006-03-30 | |
| dc.date.accessioned | 2026-07-07T07:07:22Z | |
| dc.date.available | 2026-07-07T07:07:22Z | |
| dc.description | Let $k$ be an algebraically closed field. Let $B$ be the Borel subgroup of $\mGL_n(k)$ consisting of nonsingular upper triangular matrices. Let $\frb = \mLie B$ be the Lie algebra of upper triangular $n \times n$ matrices and $\fru$ the Lie subalgebra of $\frb$ consisting of strictly upper triangular matrices. We classify all Lie ideals $\frn$ of $\frb$, satisfying $\fru' \subseteq \frn \subseteq \fru$, such that $B$ acts (by conjugation) on $\frn$ with a dense orbit. Further, in case $B$ does not act with a dense orbit, we give the minimal codimension of a $B$--orbit in $\frn$. This can be viewed as a first step towards the difficult open problem of classifying of all ideals $\frn \subseteq \fru$ such that $B$ acts on $\frn$ with a dense orbit. The proofs of our main results require a translation into the representation theory of a certain quasi-hereditary algebra $\cA_{t,1}$. In this setting we find the minimal dimension of $\mExt^1_{\cA_{t,1}}(M,M)$ for a $Δ$-good $\cA_{t,1}$--module of certain fixed $Δ$-dimension vectors. | |
| dc.description | 27 pages, 6 figures, uses epsfig, latexsym, amsfonts, amsmath, amsthm, xy | |
| dc.identifier | https://arxiv.org/abs/math/0603710 | |
| dc.identifier | http://arxiv.org/abs/math/0603710 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/110368 | |
| dc.subject | Representation Theory | |
| dc.subject | Group Theory | |
| dc.subject | 16G20, 20G05 | |
| dc.title | Prehomogeneous spaces for Borel subgroups of general linear groups | |
| dc.type | text |