https://en.wikipedia.org/wiki/Automorphic_form

(http://www.autoadmit.com/thread.php?thread_id=3022963&forum_id=2#29012873)

Algebraic topology, algebraic geometry in general. mirror symmetry, geometric rep theory, langlands program, etc are all considered hard.

(http://www.autoadmit.com/thread.php?thread_id=3022963&forum_id=2#29012898)

to a topology on E, indeed no assumption that E is a topological field. Given r there are up to isomorphism only finitely many choices for the pair (r, N) and

these can be explicitly listed without difficulty. A WD-representation (r, N) is called unramified if N = 0 and r(IQp) = {1}. It is called Frobenius semi-simple if

r is semi-simple. Any WD-representation (r, N) has a canonical Frobenius semisimplification (r, N)

ss, which may be defined as follows. Pick a lift φ of Frobp to WQp and decompose r(φ) = ΦsΦu = ΦuΦs where Φs is semi-simple and Φu is unipotent.

The semi-simplification (r, N) ss is obtained by keeping N and r|Ip unchanged and replacing r(φ) by Φs. In the case that E = Ql we call (r, N) l-integral if all the

eigenvalues of r(φ) have absolute value 1. This is independent of the choice of Frobenius lift φ.

(http://www.autoadmit.com/thread.php?thread_id=3022963&forum_id=2#29012878)

In mathematics, parabolic induction is a method of constructing representations of a reductive group from representations of its parabolic subgroups.

If G is a reductive algebraic group and P=MAN is the Langlands decomposition of a parabolic subgroup P, then parabolic induction consists of taking a representation of MA, extending it to P by letting N act trivially, and inducing the result from P to G.

(http://www.autoadmit.com/thread.php?thread_id=3022963&forum_id=2#29012992)

(When I was young, very young, they told me I was very smart. They lied.)

(http://www.autoadmit.com/thread.php?thread_id=3022963&forum_id=2#29017039)

Group theory usually refers to the study of groups in the abstract, separate from their representations. The point is that the theory is cleaner if you separate the intrinsic properties of a group (the ones that do not depend on a specific representation has a matrix group) from the ones that aren't intrinsic.

Essentially a divide and conquer approach.

You see the same principle in geometry (manifolds are defined abstractly but then embedded into Euclidean space) and algebraic geometry (brill-noether theory).

(http://www.autoadmit.com/thread.php?thread_id=3022963&forum_id=2#29258184)

http://www.cmi.ac.in/~asengupta/cv.pdf

(http://www.autoadmit.com/thread.php?thread_id=3022963&forum_id=2#29013050)

AN times E equals ABN A=1 B=5 E=3 N=0

A.

True

B.

False

try this question

(http://www.autoadmit.com/thread.php?thread_id=3022963&forum_id=2#29012942)

try this one

What is 5349 to the third power equals

A.

28,611,805

B.

28,610,803

C.

28,613,800

D.

28,611,801

(http://www.autoadmit.com/thread.php?thread_id=3022963&forum_id=2#29012970)

doesn't "AN" mean A times N?

(http://www.autoadmit.com/thread.php?thread_id=3022963&forum_id=2#29012996)

https://www.physics.harvard.edu/uploads/files/undergrad/probweek/prob57.pdf

(http://www.autoadmit.com/thread.php?thread_id=3022963&forum_id=2#29013448)

https://www.physics.harvard.edu/uploads/files/undergrad/probweek/sol57.pdf

(http://www.autoadmit.com/thread.php?thread_id=3022963&forum_id=2#29017289)