Abstract
We determine invariants like the Smith normal form and the determinant for certain integral matrices which arise from the character tables of the symmetric groups S
n
and their double covers. In particular, we give a simple computation, based on the theory of Hall-Littlewood symmetric functions, of the determinant of the regular character table χRC of S
n
with respect to an integer r≥ 2. This result had earlier been proved by Olsson in a longer and more indirect manner. As a consequence, we obtain a new proof of the Mathas’ Conjecture on the determinant of the Cartan matrix of the Iwahori-Hecke algebra. When r is prime we determine the Smith normal form of χRC. Taking r large yields the Smith normal form of the full character table of S
n
. Analogous results are then given for spin characters.
