The relation $(X+Y)^n = X^n + Y^n$, and miraculous cancellations in quantum $SL_2$
The relation $(X+Y)^n = X^n + Y^n$, and miraculous cancellations in quantum $SL_2$

Francis Bonahon, USC
Fine Hall 314
The convenient formula $(X+Y)^n = X^n + Y^n$ is (unfortunately) frequently used by our calculus students. Our more advanced students know that this relation does hold in some special cases, for instance in prime characteristic $n$ or when $YX=qXY$ with $q$ a primitive $n$root of unity. I will discuss similar ``miraculous cancellations’’ for 2by2 matrices, in the context of the quantum group $U_q(sl_2)$.