Modular Representations - Recently Updated Pages

AIM Workshop "Cohomology and Representation Theory for Finite Groups of Lie Type"

Anonymous — Mon, 06 Aug 2007 11:15:03 CDT

This site has been set up by Terrell Hodge. Currently, its purpose is to support some activities related to a June 2007 AIM workshop she is co-organizing with Chris Bendel, Cornelius Pillen, and Brian Parshall, devoted to topics associated to the modular representation theory of algebraic groups and finite groups of Lie type.

All workshop participants are invited to make changes to lists of references, accessible from the page "Reference Lists for AIM Workshop".

LiE

Anonymous — Fri, 29 Jun 2007 18:14:16 CDT

LiE can be downloaded from this link . As far as I can tell, it is only available for linux and other *nix like systems, such as Mac OS X. For those of you using Mac OS X, note the note.

Frank thinks it should be possible to compile LiE for windows using cygwin. I think so, too.

Survey Articles

Anonymous — Thu, 21 Jun 2007 20:48:51 CDT

Survey Articles

G. Hiss, Algorithms in representation theory, appearing as Section 2.8
in Computer Algebra Handbook (edited by J. Grabmeier, E. Kaltofen,
and V. Weispfenning) Springer (2003). A version of this article is available here.

E. A. O'Brien, Towards effective algorithms for linear groups, published in Finite Geometries, Groups, and Computation (edited by Hulpke, et. al.) de Gruyter (2006). A version of this article is available here.

A'. Seress, An introduction to computational group theory, Notices Amer. Math. Soc. 44 (1997). Click here to find an extended version of this article.

J.Chuang and J.Rickard, Representations of finite groups and tilting,
in Handbook of Tilting Theory (ed. L.Hugel), London Mathematical
Society Lecture Notes Series #332 (2007).

D. Joyner, A primer on computational group homology and cohomology, ArXiv
0706.0549, click here.

Go back to main reference list.

Books

Anonymous — Thu, 14 Jun 2007 15:50:03 CDT

Books

W. Bosma, J. Cannon (Eds.), Discovering Mathematics with Magma: Reducing the Abstract to the Concrete, in the Series: Algorithms and Computation in Mathematics, Vol. 19, Springer (2006). (Articles include: J.F.Carlson: Support varieties for modules.- J.F.Carlson: When is projectivity detected on subalgebras- D.F.Holt: Cohomology and group extensions in Magma.- C.M.Roney-Dougal, W.R.Unger: Computing the primitive permuation groups of degree less than 1000.)

M. Cabanes and M. Enguehard, Representation Theory of Reductive Groups, Cambridge (2004).

J. F. Carlson, L. Townsley, L. Valeri-Elizondo, M. Zhang, Cohomology
rings of finite groups. With an appendix: Calculations of cohomology
rings of groups of order dividing 64 by Carlson, Valeri-Elizondo and
Zhang. Algebras and Applications, 3, Kluwer Academic Publishers,
Dordrecht, 2003.

R. W. Carter, M. Geck (Eds.), Representations of Reductive Groups, Publications of the Newton Institute, Cambridge University Press, 1998.

C.W.Curtis and I.Reiner, Methods of Representation Theory, I & II,
Wiley (1981).

L. Evens, The Cohomology of Groups, Oxford Mathematical Monographs,
Oxford University Press, 1991.

J.E. Humphreys, Introduction to Lie Algebras and Representation
Theory, Springer-Verlag, 1972.

J. E. Humphreys, Modular Representation Theory of Finite Groups of
Lie Type, Cambridge University Press, 2006.

J. C. Jantzen, Representations of Algebraic Groups, Academic Press,
1987. 2nd ed: Math. Surveys Monographs, Vol. 107, Amer. Math. Soc.,
2003.

J. C. Jantzen, Lectures on Quantum Groups, Grad. Studies in Math. 6,
Amer. Math. Soc., 1996.

W. M. Kantor, A'. Seress, Black Box Classical Groups, Memoirs of the AMS 708, Amer. Math. Soc., 2001.

A'. Seress, Permutation Group Algorithms, Cambridge Tracts in Mathematics 152, Cambridge University Press, 2003.

Go back to main reference list.

Research Articles

Anonymous — Wed, 13 Jun 2007 14:51:35 CDT

Other Articles

Lusztig conjecture:

H.H. Andersen, J.C. Jantzen, W. Soergel,
Representations of quantum groups at a $p$th root of unity and of
semisimple groups in characteristic $p$, Ast\'erisque, 220, (1994).

Non-defining characteristic:

M. Geck and G. Hiss, Modular representations of finite groups of Lie type in non-defining characteristic, in Prog. Math. 141, Birkhauser (1997).

Magma:

W. Bosma, J. Cannon, Handbook on Magma Functions, Sydney
University, 1996.

W. Bosma, J. Cannon, C. Playhoust, The Magma Algebra System I: The
User Language, J. Symbolic Computation, 3/4, no. 24 (1997), 235-265.

Examples of Computation:

University of Georgia VIGRE Algebra Group:

1) Varieties of nilpotent elements for simple Lie algebras I: good
primes, J. Algebra, 280 (2004), 719--737.

2) Varieties of nilpotent elements for simple Lie algebras II: bad
primes, J. Algebra, 292 (2005), 65--99.

3) Support varieties for Weyl modules over bad primes, J. Algebra,
312 (2007), 602--633.

Go back to main reference list.

Reference Lists for AIM Workshop

terrell.hodge — Fri, 08 Jun 2007 18:51:15 CDT

[Note: This page is under construction. Workshop participants are invited to make additions or other changes to these pages. ]

References are grouped into pages according to the table of contents below. Please click on the links below to go to any page.

Table of Contents

Computational Packages and Projects with Computational Emphases

Computational Packages and Projects with Computational Emphases

terrell.hodge — Fri, 08 Jun 2007 16:27:39 CDT

Computational Packages and Projects with Computational Emphases

GAP homepage
Downloading GAP (the core package); for additional comments on downloading GAP, click here.
Further GAP packages for downloading.
Learning GAP4 tutorials.

MAGMA homepage.

SAGE homepage.

CHEVIE homepage.

ATLAS of Lie groups and representations homepage.

A. Buch and N. Lauritzen, The modular Lusztig conjecture in small rank. Click here.

L. Scott, Computer Investigations in Group Representation Theory (Undergraduate Research). Computations associated to the Lusztig Conjecture. Click here.

University of Georgia VIGRE Algebra Group. Click here.

Go back to main reference list.

References by Presentations/Problem Sessions at the Workshop

terrell.hodge — Fri, 08 Jun 2007 16:24:03 CDT

TBA

Go back to main reference list.

Downloading GAP

terrell.hodge — Thu, 07 Jun 2007 14:05:03 CDT

Instructions for Downloading GAP:

i. Go to http://www.gap-system.org/Download/index.html.

ii. Scroll down to “The Basic Steps of GAP Installation”, and follow the directions.

iii. NOTE: Right below the aforementioned heading, there are alternate installation options for Linux and Windows. The Windows installer includes step-by-step instructions with screen pictures, especially handy for those of us who are computer-challenged and not hip enough to have Macs.

iv. See the bottom of the webpage for “When Things Go Wrong” as needed; a local systems administrator can also help out, and workshop participants are welcome to also try contacting the organizers for assistance. Experienced users willing to lend a helping hand will also be available at the workshop.

v. The very bottom of the webpage provides a link to a very basic GAP tutorial to check out, or go directly to http://www.gap-system.org/Manuals/doc/htm/tut/chapters.htm. Further documentation, including reference manuals and other tutorial materials and links of interest are available at http://www.gap-system.org/Doc/doc.html and http://euler.slu.edu/Dept/Faculty/rainbolt/PREPtutorial.pdf.

vi. Beyond the core package, a list of additional GAP packages that may be of interest (e.g., QuaGroups for computing with quantum groups) and links for downloading them appear at http://www.gap-system.org/Packages/packages.html.