We are not major players in the tilting module world (see rather [Donkin] and references therein), but our work lends itself very well to online viewing. And thus to having a homepage. (If you, a major player, would like to be linked (or for us to house your online contribution) it would be great - let us know.)
We have a reasonably fast implementation of [Soergel]'s procedure for
computing the standard module content of tilting modules. This
implementation generates vast amounts of such data.
By virtue of the alcove geometric labelling scheme for standard module weights this data is geometric.
All else being equal, a good way to explore this geometrical data is to apply alcove geometry to a virtual reality (typically 3D in our examples).
We animate our viewing of individual tilting modules, and the iterative procedure. We do the former so that we may explore the `shape' of the tilting module in its geometric setting; we do the latter to help search for patterns of various kinds in the evolution of tilting modules as the `label' alcove moves away from the fundamental alcove.
To view some `films' of animated tilting modules you need only visit the library (under construction, but see this or this).
To explore the alcove world in which tilting modules live you need geomview.
To create your own using our `tilt' package (Copyright (C) 2000 Paul Martin and Dave Woodcock) you need a reasonably complete linux, gcc, perl etc. (see the tarball for details).
Assuming you have all the gear, it is probably enough to go into the tilt/ directory and do
But see the READMEs too.
The easiest level of configuration is to use or construct a type-specific config file called a schematum.
Examples here: schemata etc, including user contributed examples.
References and bibliography:
[Donkin] S Donkin, 1993, On tilting modules for algebraic groups, Math.Z. 212, 39-60.
[Soergel] W Soergel, 1997, Charakterformeln fur Kipp-Moduln uber Kac-Moody-Algebren, Representation Theory 1, 115-32.
[Lusztig] G Lusztig, 1980, Hecke algebras and Jantzen's generic decomposition patterns, Adv. in Math. 37, 121-164.
[MartinWoodcock] P P Martin and D Woodcock, 1998, On quantum spin-chain spectra and the structure of Hecke algebras and q-groups at roots of unity, J. Phys. A31, 10131-54.
[MartinWoodcock03] P P Martin and D Woodcock, 2003, Generalised blob algebras and alcove geometry, LMS JCM 6, 249-296.
Getting tilt to compile under gcc-3.2 required some massaging cf. the previous version. We havn't yet eliminated all the C++ ISO non-conforming warnings etc.. It's not compliant, but they're only warnings.