One of my ideas might be fruitful, or they all might have nothing to do with why representation theory connects to modular functions. Pretty much the only way to take an automorphic representation and prove that it has an associated Galois representation aktomorphic to construct a geometric object whose cohomology has both an action of the Hecke algebra and the Galois group and froups it into pieces and pick out the one you want.
Home Questions Tags Users Unanswered. AM-7Volume 7 Paul R. Probably the most notable example is aitomorphic moonshine. As you probably know, the real and imaginary parts of a holomorphic function are harmonic, i.
Such as, giving a source or writing a small exposition? More importantly, I have a basic background in the representation theory of finite groups. Well automorphoc basic link to representation theory is that modular forms and automorphic forms can be viewed as functions in representation spaces of reductive groups. AMVolume These correspondences should be nice in that adel that happen on one side should correspond to things happening on the other.
Or is it Fourier analysis on groups? An introduction to the Langlands program by Bernstein and others is also good. The point of listing ideas is to show the kind of intuition I might be looking for.
AMVolume 82 Joan S. The most comprehensive reference is the Corvallis proceedings available freely at ams. Looking for beautiful books? Home Questions Tags Users Unanswered. When you return to college in the fall, ask any of the many expert number theorists in the math department there. In fact, while recently the role of Galois representations has been highlighted Langlands program, modularity theoremthis is an entirely separate and higher level issue compared with the glbart dictionary between modular forms and automorphic representations.
The Trace Formula for GL 2 Well the basic link to representation torms is that modular forms and automorphic forms can be viewed as functions in representation spaces of reductive groups.
Cycles, Transfers, and Motivic Homology Theories. Is there a connection here? By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Atomorphicand our Terms of Service.
I also know a little bit about the basics of algebraic number theory and algebraic geometry, if that helps. But yes, to get a good understanding of the basics Lie theory is required e. AM-6Volume 6 Alonzo Church. There are numerous variations of this: More importantly, I have a basic background in the representation theory of finite groups. An introduction to the Langlands program by Bernstein and others is also good.
And if you want to get into the whole automorphic representations on adeles groups then some knowledge of algebraic groups and representations of reductive algebraic groups. Or is it just that I need to learn some more algebraic geometry? AMVolume 76 John Milnor. AMVolume Gerald B. The Classical Theory 2. I understand that Hecke characters relate to adeles, but you seem to be implying that Hecke characters lifting to characters on adeles in the first example of a classical modular grohps becoming a function on adeles.
Braids, Links, and Mapping Class Groups. The link is as follows: Hecke Theory for GL 2 oon. Sign up or log in Sign up using Google. This website uses cookies to improve your experience while you navigate through the website.
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