External Lecturer:
Ivan B. Penkov
Course Type:
PhD Course
Academic Year:
2024-2025
Period:
October - November
Duration:
20 h
Description:
The course will consist of two parts, roughly ten hours each. The first part will start with a brief recollection of basics from the representation theory of classical finte-dimensional Lie algebras, followed by an introduction to Lie algebras of infinite matrices. The main topic of the fist part will be a discussion of the categories of tensor modules over Mackey Lie algebras.
The second part will start with tthe classical Bott-Borel-Weil Theorem. Next we will discuss homogeneous ind-spaces of the finitary classical ind-groups. At the end of the course we will present an analogue of Bott-Borel-Weil's Theorem for classical ind-groups.
Recommended literature
1.W. Fullton, J. Harris, Representation theory: a first course, Springer Verlag.
2. I. Penkov, C. Hoyt, Classical Lie algebras at infinity, Springer Verlag.
Research Group:
Location:
133 on Tuesday, 136 on Wednesday