Abstract These lectures will explore connections between (generalized) q-Schur algebras and the quantized enveloping algebra Uq(g) associated with a simple Lie algebra g. These connections are facilitated by a certain completion of Lusztig’s modified form of Uq(g). Although the q-Schur algebras arose initially as quotients of Uq(g) it is possible to reverse history and use them as a tool to re...
PrerequisiteSome knowledge of representation theory of Lie groups or symmetric group and random matrix theory would be helpful. Demonstrations require the use of Python programming language and Sage computer algebra system, so some experience here would be a plus. There is some overlap with material of my previous course "From free fermions to limit shapes and beyond" and connections to the cou...