Séminaire Lotharingien de Combinatoire, 95B.39 (2026), 12 pp.
Beth Anne Castellano, Rosa Orellana and Mike Zabrocki
Transition Matrices for cCharacter Bases of the Symmetric Group
Abstract.
We consider inhomogeneous bases of symmetric functions which evaluate to characters of the symmetric group
and are closely related to long-standing open problems in combinatorial representation theory
such as the Kronecker problem and the restriction problem.
We describe combinatorial interpretations for the transition matrices between the basis that evaluates to
induced trivial characters (or permutation characters) and other classical bases of symmetric functions.
The transition coefficients are closely related to the Möbius function of
the multiset partition poset and are expressed in terms of multisets of Lyndon words.
Received: November 15, 2025.
Accepted: February 15, 2026.
Final version: April 1, 2026.
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