most recent 30 from http://mathoverflow.net 2013-05-24T05:02:50Z http://mathoverflow.net/feeds/question/40305 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/40305/bernsteins-presentation-for-the-hecke-algebra unknown (google) 2010-09-28T12:29:01Z 2010-10-01T09:40:28Z

<p>Any one know of any good references for reading about the Bernsteins Presentation of the Iwahori Hecke Algebra? I need some notes which has an example or two. It would really help. </p>

http://mathoverflow.net/questions/40305/bernsteins-presentation-for-the-hecke-algebra/40318#40318 Bugs Bunny 2010-09-28T14:02:42Z 2010-09-28T19:49:44Z

<p>MathSciNet search for Hecke and Bernstein Presentation gives <a href="http://www.ams.org/mathscinet-getitem?mr=1922389" rel="nofollow">this</a> ...</p>

http://mathoverflow.net/questions/40305/bernsteins-presentation-for-the-hecke-algebra/40328#40328 Jim Humphreys 2010-09-28T15:23:58Z 2010-09-28T15:52:42Z

<p>Like some of his other important ideas, Bernstein's presentation has mostly been disseminated through the papers of other people. Probably the most influential is the 1989 JAMS paper by Lusztig, freely available from the AMS <a href="http://e-math.ams.org/journals/jams/1989-02-03/S0894-0347-1989-0991016-9/home.html" rel="nofollow">here</a>. Combinatorial work by Arun Ram and others involving affine Hecke algebras also depends on this viewpoint: see for example <a href="http://front.math.ucdavis.edu/0807.3602" rel="nofollow">Parkinson-Ram</a></p> <p>Two relevant recent papers with extensive references are also available on arXiv and would be worth looking at in any case: <a href="http://front.math.ucdavis.edu/0201.5176" rel="nofollow">haines-pettit</a> and <a href="http://front.math.ucdavis.edu/0610.5839" rel="nofollow">goertz</a>.</p>

http://mathoverflow.net/questions/40305/bernsteins-presentation-for-the-hecke-algebra/40712#40712 Amritanshu Prasad 2010-10-01T04:09:43Z 2010-10-01T04:09:43Z

<p>I found the paper of Chriss and Khuri-Makdisi (Chriss, Neil; Khuri-Makdisi, Kamal. On the Iwahori-Hecke algebra of a $p$-adic group. Internat. Math. Res. Notices 1998, no. 2, 85--100.) quite helpful.</p> <p>You may also look at <a href="http://arxiv.org/abs/math.RT/0309168" rel="nofollow">Haines-Kottwitz-Prasad</a> and <a href="http://arxiv.org/abs/math/0504417" rel="nofollow">Prasad</a>.</p>

http://mathoverflow.net/questions/40305/bernsteins-presentation-for-the-hecke-algebra/40726#40726 Sheikraisinrollbank 2010-10-01T09:19:35Z 2010-10-01T09:40:28Z

<p>In book form, the equivalence of the Coxeter and Bernstein presentations of the affine Hecke algebra appears in the first 4 chapters of Macdonald's book "Affine Hecke algebras and orthogonal polynomials". It is very carefully written, but the notation can get a bit heavy. When first reading it, I suggest you always assume that you are in case (1.4.1) in Macdonald's notation.</p> <p>Chapter 6 does rank one examples.</p>