Factorization of Classical and Universal Characters Twisted by Roots of Unity
New identities showing that the irreducible characters of the classical groups (GL, Sp, O, SO), when their variables are twisted by an odd power of an even primitive root of unity, factor into products of characters of smaller classical groups indexed by the core and quotient of the partition, with the analogous specialization extended to Koike-Terada universal characters, which then take only the values 0, plus or minus 1, and plus or minus 2.
2501.00275
This paper proves new factorization identities for the irreducible characters of the classical families of groups (general linear, symplectic, and orthogonal) when their variables are specialized at …