IntroSurvey of representation theory. (English) Zbl 1542.81479
Summary: There could be thousands of Introductions/Surveys of representation theory, given that it is an enormous field. This is just one of them, quite personal and informal. It has an increasing level of difficulty; the first part is intended for final year undergrads. We explain some basics of representation theory, notably Schur-Weyl duality and representations of the symmetric group. We then do the quantum version, introduce Kazhdan-Lusztig theory, quantum groups and their categorical versions. We then proceed to a survey of some recent advances in modular representation theory. We finish with 20 open problems and a song of despair.
MSC:
| 81R05 | Finite-dimensional groups and algebras motivated by physics and their representations |
| 81R10 | Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations |
| 20G05 | Representation theory for linear algebraic groups |
| 81R50 | Quantum groups and related algebraic methods applied to problems in quantum theory |
| 20C20 | Modular representations and characters |
| 81-02 | Research exposition (monographs, survey articles) pertaining to quantum theory |
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