5 papers
A skew Murnaghan--Nakayama rule for Hopf dual pairs
Naihuan Jing, Ning Liu
We develop a uniform skew Murnaghan--Nakayama theory for graded Hopf dual pairs equipped with a nondegenerate Hopf pairing. Using the completed Cauchy element, its grouplike factor…
Dual Murnaghan-Nakayama rule for Hecke algebras in Type
Naihuan Jing, Ning Liu, Yu Wu
Let be the value of the irreducible character of the Hecke algebra of the symmetric group on the conjugacy class of type . The usual Murnaghan-Nakayama rule…
Murnaghan-Nakayama rule for the cyclotomic Hecke algebra and applications
Naihuan Jing, Ning Liu
We establish a Murnaghan--Nakayama rule for the irreducible characters of the cyclotomic Hecke algebra on Shoji's standard elements. Combined with Shoji's d…
On a Pieri-like rule for the Petrie symmetric functions
Emma Yu Jin, Naihuan Jing, Ning Liu
A -ribbon tiling is a decomposition of a connected skew diagram into disjoint ribbons of size . In this paper, we establish a connection between a subset of -ribbon tiling…
Irreducible characters and bitrace for the -rook monoid
Naihuan Jing, Yu Wu, Ning Liu
This paper studies irreducible characters of the -rook monoid algebra using the vertex algebraic method. Based on the Frobenius formula for , a new iterative ch…