Notes 2007

Arun Ram
Department of Mathematics
University of Wisconsin, Madison
Madison, WI 53706 USA

Last updated: Thursday 28-Jun-2007

Many pages on this site use MathML. These pages are UNDER CONSTRUCTION. To view these pages use a Mozilla browser like Firefox or Camino (optimised for Macintosh). These are MathML and SVG capable. Download the necessary fonts from MathML at MIT or the appropriate font installer in the right hand column of the fonts for MathML enabled Mozilla. Test your browser with the MathML torture test.

Most of the material on this site is the result of research and teaching intiatives supported by the National Science Foundation under Grant No. 0353038. I thank National Science Foundation for continuing support of my research. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.

These MathML pages were developed with the help of Rahbar Virk at University of Wisconsin.


Material related to the AIM workshop on Buildings and Combinatorial Representation Theory .
Additional material for this workshop is available at
Kac-Moody algebras
Chevalley groups
The Flag variety
Loop groups
The affine Flag variety
Affine Hecke algebras
Central Extensions


Other notes
Reflection groups
Simplicial complexes
Homology and derived functors
Koszul and de Rham complexes
Homotopy theory
pdf of some handwritten computation of Verma modules for quantum groups of type A1
an html version of Work2007/Bites2007/mmtmpbite10.10.06.tex
an early xml version of some material on moment maps


How to do Proofs
Presentation Markup MathML summary
MathML Character Guide