Stephen R Doty

Professor Emeritus of Mathematics & Statistics, Computer Science

Contact
  • Email: doty AT math DOT luc DOT edu, sdoty AT luc DOT edu.

  • Mailing address: (Anything important should be sent by email.)

    Department of Mathematics and Statistics, Loyola University Chicago, Chicago, IL 60660 USA.

Research

I’m interested in algebraic representation theory, including for instance representations of:

  • algebraic groups
  • finite-dimensional algebras
  • groups of Lie type
  • Lie algebras
  • quantum groups.

Some specialized topics of interest include:

  • Schur-Weyl duality
  • Schur algebras
  • Hecke algebras
  • quasihereditary algebras
  • cellular algebras
  • diagram algebras
  • quantized enveloping algebras.
Preprints

My preprints on the arXiv.

Publications
Vitae
  • Currently: Professor Emeritus, Loyola University Chicago
  • 1994-2020: Professor, Loyola University Chicago
  • 1987-1994: Assistant and Associate Professor, Loyola University Chicago
  • 1985-1987: Kenna Assistant Professor, University of Note Dame
  • 1982-1985: Acting Assistant Professor, University of Washington
  • 1982: PhD, Mathematics, University of Notre Dame (Advisor: W J Wong)
Weyl modules: GAP Package

A GAP package supporting computations with Weyl modules and simple modules for a given simply-connected, semisimple, algebraic group in positive characteristic. The package computes submodule structure, simple characters, and decomposition numbers. The package also has some (limited) support for Schur algebras and symmetric groups. Current version is Version 1.1.

To try the software, download the GAP-files (a zip archive) and unpack it somewhere. It should unpack into three files (weyl.g, weylmod.gd, and weylmod.gi). From the same folder where you unpacked those files, initiate GAP by typing:

$ gap weyl.g

in a command shell. This will load the package into GAP’s memory, and you should now be able to test the commands. Alternatively, you can start a GAP session as usual and then load the package by typing the GAP command:

gap> Read( "weyl.g" );

if you initiated the GAP session from the same folder containing the file “weyl.g”. If not, you will need to tell GAP what path to use or specify a pathname on the Read command (and perhaps edit the file “weyl.g” to contain correct pathnames as well).

Please report any problems.

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