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1. Assume that the field is algebraically closed and has zero characteristic, G is finite and representations are finite-dimensional.
Show that this statement is true under the above assumptions:
"Let p be an irreducible representation of G, and q be an irreducible representation of H. Is it always true that the exterior tensor product of p and q is an irreducible representation of G X H?"
2. Let p: G -> GL(V) be a representation. Show that each irreducible subrepresentation of V has multiplicity 1 iff EndG(V) is a commutative ring.
Example of a Random Procedure with Specified Events. Please list as many different groups of complete events as possible for an experiment of your choice (Probability). Need real world example on complete events
Suppose that a pair of 20-sided dice are rolled (the sides are numbered 1-20). What is the probability that the sum of the dice is 13?
Conditional Probability Example I'm trying to set up an excel spreadsheet to solve a statistical probability.Patients 23% (smokers) -18% have a chance of contracting a serious illness
Poisson Kernel and Harmonic Function, Let P_r(t)=R((1+z)/(1-z)), z=re^it be the Poisson kernel for the unit disc |z|
When she is 30, Sue starts making annual deposits of $2,000 into a bondfund that pays 8% annual interest compounded continuously. Assuming that her deposits are made as a contiuous income flow, how much money will be in her account if she retires ..
Differentiate between a function and a linear function. Describe the mathematical equation of a standard linear function. Describe how to compute the slope of a line.
Calculate the reduced row echelon form of the following matrices. Approximate answers should be entered to at least 4 decimal places.
Determine forecasts value
Determine the p-value for testing
Solve the given integral by the method of partial fractions: (S stands for the integration sign) S sec^2(x) / (tan^3(x) - tan^2(x)) dx
Suppose you are going to flip a coin once. What is the set of possible outcomes for this? Suppose you are going to flip a coin twice. What is the set of possible outcomes for this?
There are 3 suspects, A, B, and C, for a robbery that presumably happened in a shop. We know that the following facts are true:
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