Processing math: 100%

Quiz description

You should show all of your calculations and explain what you are doing.
You may use a calculator to do arithmetic, but the use of software packages like Mathematica, Sage, etc to solve problems is not allowed

Submit your answer

After you have completed the quiz, please save, scan, or take photos of your work and upload your files to the questions below. Crowdmark accepts PDF, JPG, and PNG file formats.

Problem 1. 1. Consider the cyclic group Gn=xxn=1.
a) Describe all one-dimensional complex representations of Gn.
b) Prove that every complex representation of Gn has a one-dimensional invariant subspace.
Problem 2. 2. a) Prove that there is a two-dimensional representation of G4 such that
x(0110)
b) Find all invariant subspaces for the corresponding real representation.
c) Find all invariant subspaces for the corresponding complex representation.
Problem 3. 3. Consider the standard two-dimensional representation of the dihedral group Dn. For which n is this an irreducible complex representation.
数论代写请认准UpriviateTA

数论代写请认准UpriviateTA. UpriviateTA为您的留学生涯保驾护航。

Categories: 数学代写数论