Comments on: looking for the moonshine picture http://www.neverendingbooks.org/index.php/looking-for-the-moonshine-picture.html lieven le bruyn's blog Fri, 20 Jan 2012 16:50:41 +0100 hourly 1 http://wordpress.org/?v=3.3.1 By: John McKay http://www.neverendingbooks.org/index.php/looking-for-the-moonshine-picture.html/comment-page-1#comment-8757 John McKay Mon, 08 Mar 2010 18:45:28 +0000 http://www.neverendingbooks.org/?p=1728#comment-8757 <p>John Conway's paper: On understanding \Gamma_0(N)^{+} is generalized to the Q-lattices of Connes - Marcolli - Chapter 3 of their book (go to Connes home page) - and specially Section 3 page 452. Much is ripe for the picking.</p> John Conway’s paper: On understanding \Gamma_0(N)^{+} is generalized to the Q-lattices
of Connes – Marcolli – Chapter 3 of their book (go to Connes home page) – and specially Section 3 page 452. Much is ripe for the picking.

]]> By: lieven http://www.neverendingbooks.org/index.php/looking-for-the-moonshine-picture.html/comment-page-1#comment-8086 lieven Tue, 12 May 2009 11:47:28 +0000 http://www.neverendingbooks.org/?p=1728#comment-8086 <p>John : it looks to me that the largest cells in the moonshine picture might have dimension 3. Or is this not the case? Also, i do not know how many vertices it has. There is no 1-1 between vertices (lattices) and moonshine groups (which act on some subsets of vertices).</p> <p>D. Eppstein : that would be nice, though i dont know why this should be the case.</p> John : it looks to me that the largest cells in the moonshine picture might have dimension 3. Or is this not the case? Also, i do not know how many vertices it has. There is no 1-1 between vertices (lattices) and moonshine groups (which act on some subsets of vertices).

D. Eppstein : that would be nice, though i dont know why this should be the case.

]]> By: John McKay http://www.neverendingbooks.org/index.php/looking-for-the-moonshine-picture.html/comment-page-1#comment-8085 John McKay Tue, 12 May 2009 11:30:36 +0000 http://www.neverendingbooks.org/?p=1728#comment-8085 <p>The number of monstrous moonshine arithmetic subgroups of PSL(2,Z) is 171. This is the binomial coefficient 19C2. Perhaps we are looking at edges in a 19-dim space ?</p> The number of monstrous moonshine arithmetic subgroups of PSL(2,Z) is 171. This is the binomial coefficient 19C2. Perhaps
we are looking at edges in a 19-dim space ?

]]> By: D. Eppstein http://www.neverendingbooks.org/index.php/looking-for-the-moonshine-picture.html/comment-page-1#comment-8082 D. Eppstein Mon, 11 May 2009 18:15:59 +0000 http://www.neverendingbooks.org/?p=1728#comment-8082 <p>(1-skeletons of) Cartesian products of trees are examples of <a href="http://en.wikipedia.org/wiki/Median_graph" rel="nofollow">median graphs</a>. So I guess for any three equivalence classes of commensurable lattices there is a well defined equivalence class of lattices median between the three. Do you know whether the moonshine picture is likely to also be a median graph? That is, is it closed under these median operations?</p> (1-skeletons of) Cartesian products of trees are examples of median graphs. So I guess for any three equivalence classes of commensurable lattices there is a well defined equivalence class of lattices median between the three. Do you know whether the moonshine picture is likely to also be a median graph? That is, is it closed under these median operations?

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