Once you have a matrix representation of any group, a 1-D representation can be obtained by taking the determinants of the matrices. Show that the multiplicative relations are preserved in this determinant representation. (a) (b) Use determinants to obtain a 1-D representation of D3 from the 2 x 2 representa- tion in Eq. (17.2).
Once you have a matrix representation of any group, a 1-D representation can be obtained by taking the determinants of the matrices. Show that the multiplicative relations are preserved in this determinant representation. (a) (b) Use determinants to obtain a 1-D representation of D3 from the 2 x 2 representa- tion in Eq. (17.2).
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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Transcribed Image Text:Here is a unitary representation of the group D3 illustrated in Fig. 17.2:
U(1) =
U(C3) =
U(C}):
U(C2) =
%3D
-1
U(C):
U(C;) = (
(17.2)
Transcribed Image Text:17.2.4
(a) Once you have a matrix representation of any group, a 1-D representation can be
obtained by taking the determinants of the matrices. Show that the multiplicative
relations are preserved in this determinant representation.
(b) Use determinants to obtain a 1-D representation of D3 from the 2 x 2 representa-
tion in Eq. (17.2).
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