Howe Duality Over Finite Fields

Explore the complete decomposition of oscillator representations under tensor embeddings of symplectic and orthogonal group products over finite fields through Roger Howe's correspondence framework in this 59-minute mathematical lecture. Delve into Sophie Kriz's comprehensive analysis that provides applications including a proof of the rank conjecture and addresses a very stable case of the character sum conjecture proposed by Shamgar Gurevich and Roger Howe. Learn about the innovative approach based on studying endomorphism algebras from the perspective of tensor category interpolation, offering new insights into representation theory over finite fields. Gain understanding of advanced topics in group theory, representation theory, and algebraic structures as presented at this Special Joint IAS/PU Group Theory Afternoon session at the Institute for Advanced Study.