In 2014 George Lusztig asked if there are “higher generations of quantum groups” that further extend the approximation of the representation theory of algebraic groups in positive characteristics by quantum groups at roots of unity. One approach towards an answer is to employ cohomology theories of higher chromatic height (quantum groups correspond in a precise way to height 1, the modular representation theory to height infinity). So far there is no definition of these higher generation quantum groups, yet I would like to report on recent progress towards a solution in type A1. This is joint work with Yaping Yang and Gufang Zhao.

Place: Room 204, RIMS