A recursion formula for the irreducible characters of the symmetric group

2017/12/21 by Randall R. Holmes, Holmes, Randall R.
Mathematics · Computer Science · #Stochastic processes and statistical mechanics #Algorithms and Data Compression #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1712.08023

Abstract

The branching theorem expresses irreducible character values for the symmetric group S_n in terms of those for S_n-1, but it gives the values only at elements of S_n having a fixed point. We extend the theorem by providing a recursion formula that handles the remaining cases. It expresses these character values in terms of values for S_n-1 together with values for S_n that are already known in the recursive process. This provides an alternative to the Murnaghan-Nakayama formula.

Related

• Irreducible characters of the generalized symmetric group
• The Murnaghan-Nakayama rule and some virtual S_n characters
• A conjectured combinatorial interpretation of the normalized irreducible character values of the symmetric group
• Irreducible Symmetric Group Characters of Rectangular Shape
• Branching rules for the Weyl Groups of the Unitary and Orthogonal Lie\n Groups