Group 13 elements reactivity with halogens
This is due to the Inert Pair Effect. As we move down the 13th group, addition of d orbitals and f orbitals are taking place. Since the d orbitals and f orbitals are away from the nucleus, they have poor sheilding power or capability and thus the s orbitals of the outermost shell are attracted towards the nucleai, making it difficult for s orbital electrons to leave the orbitals and only pairing of the 1 electron in p orbital is possible. Thus +1 valency of Tl is more stable than +3 as it is not energetically favored. This,ofcourse, does not mean that formation TlI3 is not possible. It's just that it requires more energy.