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:

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

    (Anything important should be sent by email)

Curriculum 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)

Lecture Notes on Abstract Algebra Lecture Notes in Abstract Algebra is a textbook for a first undergraduate course in abstract algebra. It is free and open source.

Here is the PDF file.

The book is published under a Creative Commons (CC BY 4.0) license, which means that you can distribute, remix, adapt, and build upon the material for any purpose, even commercially, as long as you give appropriate credit, provide a link to the license, and indicate if changes were made.

This book is open source, which means that the  source code is freely available on the author’s GitHub page, at github.com/srdoty/AbstractAlgebraBook.

Research Interests 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.

Research Preprints

My preprints on the arXiv.

Research Publications

Weyl modules: GAP Package

A GAP package supporting computations with Weyl modules and simple modules for a given simply-connected simple algebraic group in positive characteristic. The package computes simple characters, decomposition numbers, and structural information. The package also has some (limited) support for Schur algebras and symmetric groups. The latest version is Version 2.1.

Instructions for Versions before 2.0 only!

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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