DATE2019-12-12 16:10-17:00


SPEAKER佐藤僚 博士(中央研究院數學研究所

TITLECommutant Constructions in Representation Theory

ABSTRACT For an algebra $A$ and its subset $B$, the commutant algebra $Com(B,A)$ is defined as the set of elements in $A$ which commute with all elements of $B$. If we know much about the representation theory of $A$ and $B$, we obtain lots of information about that of $Com(B,A)$ (e.g. irreducible representations, characters, fusion rules, etc.). In this talk, we focus on the case that $A$ and $B$ are the universal enveloping algebraof certain Lie superalgebras associated with simple Lie algebras. We discuss some relationship between the representation theory of asimple Lie algebra and that of the corresponding commutant algebra.