The same parity of K-types occurring in an irreducible representation
主 题: The same parity of K-types occurring in an irreducible representation
报告人: Dr. Xiang FAN (School of Mathematical Science, PKU)
时 间: 2014-12-09 13:45-14:45
地 点: Room 77201 at #78 courtyard, Beijing International Center for Mathematical Research（博士后讨论班）
Branching laws and invariant theory are two hot topics in the representation theory of Lie groups. In this talk, the speaker will show an interesting branching phenomenon (valid for most classical Lie groups) which reveals some relations between these two topics. The phenomenon is that all K-types occurring in an irreducible admissible representation have the same parity. Here K is a maximal compact subgroup, and the “parity” means the parity of the sum of integral coefficients parametrizing the highest weight of the K-type (amended with information on signs if K is disconnected). This phenomenon can be proved by Howe's duality theory for reductive dual pairs, and comes down to an outcome of classical invariant theory.
