ADVANCED MATHEMATICS IS INCREDIBLY COMPLEX--HOW DO PEOPLE EVEN FATHOM THIS STUFF
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Poast new message in this thread
Date: October 21st, 2015 10:58 AM Author: clear half-breed
The key point here is that there is no reference
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) |
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Date: October 21st, 2015 11:15 AM Author: clear half-breed
can you explain this?
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)
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Date: November 26th, 2015 6:36 PM Author: Bateful magenta heaven electric furnace
Matrix groups were the original physics context where this stuff first appeared iitc.
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) |
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Date: October 21st, 2015 11:07 AM Author: clear half-breed
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) |
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Date: October 21st, 2015 11:11 AM Author: clear half-breed
nice brother.
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)
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