praharmitra said:Hi,
I am currently studying Lie Algebra in Particle Physics' by Howard Georgi. I am finding the notes on Weights and Roots quite confusing. Can anyone suggest another book which explains this bit in a better fashion?
torquil said:If you are mathematically inclined, this is a good one:
Hsiang - Lectures on Lie groups
Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces. It has applications in many areas of mathematics, including group theory, algebraic geometry, and number theory.
Books in representation theory provide a comprehensive and in-depth understanding of the subject, covering its foundations, developments, and applications. They serve as valuable resources for researchers, students, and educators, helping them to gain a deeper understanding of the theory and its applications.
Some common topics covered in books on representation theory include group representations, Lie algebras, character theory, representation rings, and their applications in physics, chemistry, and other fields. They also often discuss related topics such as representation categories, homological methods, and geometric representation theory.
Books on representation theory can benefit a wide range of readers, including mathematicians, physicists, chemists, and researchers in other fields. They can also be useful for students at the undergraduate and graduate levels who are interested in learning about abstract algebra and its applications.
Yes, there are several highly recommended books on representation theory, including "Representation Theory: A First Course" by William Fulton and Joe Harris, "Representation Theory of Finite Groups" by Benjamin Steinberg, and "Introduction to Representation Theory" by Pavel Etingof, et al. It is also recommended to consult with a mathematics advisor or colleague for personalized recommendations based on individual interests and level of expertise.