In this talk, we first present our study on the number of partitions of a positive integer m into at most n parts in a given set A. We prove that such a number is bounded by the nth Fibonacci number F(n) for any m and some family of sets A including sets of powers of an integer. Then we use this result to estimate the cohomology space of the simple algebraic group SL2 with coefficients in Weyl modules. In particular, let k be an algebraically closed field of prime characteristic p and V(m) the Weyl SL2-module of highest weight m. We show that for p ≥ 5, dim Hn(SL2,V(m))≤ F(n+1) for all m,n ≥ 0.
This is joint work with S. Benzel, S. Conner, and K. Pham.
This video is part of the University of Georgia‘s Algebra seminar.
