Representations of finite groups
Representations of finite groups
Representations of finite groups [MAL7380] (3 Credits)
Prerequisites : Linear Algebra (MAL6010) and Abstract Algebra (MAL6040)
Monday : 3:00-3:40 PM
Tuesday : 9:00- 9:40 AM
Wednesday : 2:00-2:40 PM
Thursday : 8:00- 8:40 AM
Friday: 1:00-1:40 PM
Internal -60 %
Assignments- 10%
Quiz- 10%
Presentations- 10%
Projects-15%
Viva-Voce – 15%
External-40% (End trimester Examination)
The quizzes will be taken on Dec 12, Dec 26, Jan 8, Jan 22, and Feb 5.
The Presentations will be taken on Dec 11, Dec 18, Jan 1, Jan 15, and Jan 30.
Group Action and Modules[6 Lectures]: Groups and Examples (Recall), Group action, Conjugacy Classes, Modules: Definition and Examples.
Basic concepts of Representation Theory[10 Lectures]: Representations and basic examples, FG-modules, Group algebra, Irreducible representations, complete reducibility and Maschke’s theorem, Schur’s lemma.
Characters and Burnside’s pq Theorem[10 Lectures]: Character theory of representations, orthogonality relations, decomposition of the regular representation. Character Tables of some groups, Characters and Algebraic Integers, Burnside’s pq-theorem.
Representation theory of symmetric groups[16 Lectures]: Restriction of a representation, induced representations, Frobenius reciprocity, Mackey’s irreducibility criterion, Representation theory of symmetric groups, Few applications of Representation Theory (if time permits).
Benjamin Steinberg, Representation Theory of Finite Groups, Springer (Universitext), 2012.
Gordon James and Martin Liebeck, Representations and Characters of Groups, Cambridge University Press, 2001.
William Fulton and Joe Harris, Representation Theory: A First Course, Springer (Graduate Texts in Mathematics 129), 1991.
Amritanshu Prasad, Representation Theory: A Combinatorial Viewpoint, Cambridge University Press, 2015.
Conjugacy Classes and Characters of Dihedral Groups [Shivani Agarwal, Jyoti Deshwal, Apoorva Lakshman]
Character table of GL(2,q) [ N. R. Rohan, Vishal, Tushar Badola]
Conjugacy Classes and Characters of Groups of order p^3 and of order16 [Ajay Kumar, Pankaj Yadav, Jashan]
Conjugacy classes and Characters of groups of order pq [Vaibhav Agarwal, Md. Umar faruq Ali, Pramod Kalal]
Fourier Analysis on finite groups [Pushpendra Singh, Ratnesh kumar singh, Ruby]
An application of representation theory to molecular vibration [Sushmita Yadav, Shivani, Sanghdeep Kishor Ukey]
Conjugacy Classes and Characters of Alternating Groups[Harshita, Arnab Kayal, Shubham Garg]
Probability and Random Walks on Groups[Nammi Venkata apparao, Ayush agarwal, Naveen Kumar]
Character Table of simple group of order 168 [Adarsh Dwivedi, Sabhilesh, Ankit chauhan]
Another Theorem of Burnside (Real Representations) [Rhondeno Murry, Alka Santosh, Himanshi Bansal]
The Centralizer Algebra and Gelfand Pairs[Deepak Kumar Mahanta, Deepanshu Dhawan]