Math
662--Section 500 -- Spring 2011
Representation Theory of
Finite Groups
TR 2:20-3:35pm
BLOC 624
http://www.math.tamu.edu/~rowell/M662-Spring11.html
Homework: (turn in all problems) unless otherwise stated, all
representations are finite dimensional vectors spaces over an
algebraically closed field of characteristic 0 and G is a finite group.
- HW1: (due Feb. 10) 1.
show that if (f,V) is a representation of G then f(g) is diagonalizable
for elements g in G. 2. Show that the symmetric and alternating
squares of a representation V are G-stable (dim(V) and G finite).
- HW2: (due Feb. 17) HW2662.pdf
- HW3: (due Feb. 24) HW3662.pdf
- HW4: (due March. 3) HW4662.pdf
- HW5: (due March 10) 1. show that if
K<H<G are subgroups and (phi,W) is a representation of K then
Ind_H^G(Ind_K^H(W)) is isomorphic to Ind_K^G(W) (i.e. the operation of
inducing representations is transitive. 2. Consider the index 2
subgroup H=<1,-1,i,-i> of the quaternion group Q_8. Observe
that H is isomorphic to the cyclic group C_4. Determine the
decomposition of the Q_8 represetations induced fromthe two H-representations determined by i->-1 and i->(sqrt(-1)).
- HW6: (due March 24): HW6662.pdf
- HW7: (due March 31): HW7662.pdf
- HW8: (due April 7): HW8662.pdf
HW8662sols.pdf
- HW9: (due April 14): HW9662.pdf
- HW10 (due April 28): HW10662.pdf
Course Description:
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This course is an introduction to the
theory of complex representations of finite groups.
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Course Information:
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Instructor:
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Dr.
Eric Rowell
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Office Hours:
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TBA |
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Office:
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210 Milner
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Office Phone:
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845-2833
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E-mail:
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rowell@math.tamu.edu
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Textbooks:
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Serre,
Linear Representations of Finite Groups (not required)
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Course Syllabus:
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We
will cover most of chapters 1-3 and 5-7 with additional topics from
other sources.
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Exams:
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No
exams |
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Homework:
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Written homework will be due on a sporadic
basis.
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Prerequisites:
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M653 or equivalent and some
familiarity with linear algebra.
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Course Webpage:
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http://www.math.tamu.edu/~rowell/M662-Spring11.html
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Grading:
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Your final grade will be based upon the
graded HW assignments
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Course Policies:
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Missed Work:
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Making up missed work will be arranged according to University
policies only. See Student Rule 7 for a description of university
approved excuses:
http://student-rules.tamu.edu/rule07
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Academic Dishonesty:
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It is not permissible to hand in the work of
others for a grade. You are allowed to discuss homework with others,
but your write-ups are expected to be done on your own and in your own
words. Copying the work of others may be prosecuted to the full extent
possible under University policies.
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Disability Assistance:
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Assistance is available from the office of
Services for Students with Disabilities, Koldus 126, 845-1637, disability@tamu.edu, http://disability.tamu.edu/.
Students seeking special considerations for an exam must contact this
office several weeks in advance.
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Page maintained by Eric
Rowell,
Dept. of Mathematics, Texas A&M University.