Check that p is a representation of V. (i) (ii) Find the character of p. (iii) Is p irreducible ? Justify. .

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let V= {e,a,b,c} be the klein four group with
the group operation given below :
e
a | b| c
е
е
a
b
a
a
е
b
b|b
e
a
c| b
a
е
Let p: V→GL2 (C) be defined as
1
p (e):
p (a)
-1
0.
0.
P (b) =
-1
-1
(i)
Check that p is a representation of V.
Find the character of p.
(ii)
(iii) Is p irreducible ? Justify.
Transcribed Image Text:Let V= {e,a,b,c} be the klein four group with the group operation given below : e a | b| c е е a b a a е b b|b e a c| b a е Let p: V→GL2 (C) be defined as 1 p (e): p (a) -1 0. 0. P (b) = -1 -1 (i) Check that p is a representation of V. Find the character of p. (ii) (iii) Is p irreducible ? Justify.
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