My OperaActions...
Wednesday, December 7, 2005 11:51:03 PM
... for the rest of the week.
#1,
Exercise 3.24. Let H = A_5 subset of G = S_5. Show that: lnd U = U (+) U', lnd V = V (+)V', and Ind W = W (+) W', whereas Ind Y = Ind Z = ^2V.
Exercise 3.25*. Which irreducible representations of S_n remain irreducible when restricted to A_d? Which are induced from A_d? How much does this tell you about the irreducible representations of A_d?
Exercise 3.26*. There is a unique nonabelian group of order 21, which can be realized as the group of affine transformations x -> ax+b of the line over the field with seven elements, with a a cube root of unity in that field. Find the irreducible representations and character table for this group.
( That should give an idea if I comprehended things sofar. )
#2,
Startup of 'Polyhedra Inspector'.
#1,
Exercise 3.24. Let H = A_5 subset of G = S_5. Show that: lnd U = U (+) U', lnd V = V (+)V', and Ind W = W (+) W', whereas Ind Y = Ind Z = ^2V.
Exercise 3.25*. Which irreducible representations of S_n remain irreducible when restricted to A_d? Which are induced from A_d? How much does this tell you about the irreducible representations of A_d?
Exercise 3.26*. There is a unique nonabelian group of order 21, which can be realized as the group of affine transformations x -> ax+b of the line over the field with seven elements, with a a cube root of unity in that field. Find the irreducible representations and character table for this group.
( That should give an idea if I comprehended things sofar. )
#2,
Startup of 'Polyhedra Inspector'.
