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A Morris recursion rule for values of the spin characters of wreath products

  • Rijubrata Kundu
  • Papi Ray
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Abstract

The classical Murnaghan-Nakayama rule is a recursive formula for computing the values of complex irreducible characters of the symmetric group Sn. Alun Morris proved a recursive formula for evaluating the values of irreducible spin characters of S̃n, where S̃n is one of the Schur covers of Sn defined by S̃n:=⟨ t1,t2,⋯,tn−1,z | z2=1, ti2=z, (titi+1)3=z, titj=ztjti if |i−j|>1⟩. A recursive formula for evaluating the values of complex irreducible characters of the wreath product Gwr Sn, where G is a finite group, was proved by J. Stembridge. In this article, we state and prove a recursive formula to compute the values of the irreducible spin characters of the wreath product Gwr S̃n. For the convenience of implementing these recursive formulas, we extend the notion of 0-1 boundary sequence of a Young diagram to shifted Young diagrams.

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Cite

BibTeXRIS
BibTeX
@misc{kundu2026morris,
  title = {{A Morris recursion rule for values of the spin characters of wreath products}},
  author = {Rijubrata Kundu and Papi Ray},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.06558},
  eprint = {2610.06558},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.06558},
}
RIS
TY  - UNPB
TI  - A Morris recursion rule for values of the spin characters of wreath products
AU  - Rijubrata Kundu
AU  - Papi Ray
PY  - 2026
DA  - 2026/10/05
PB  - arXiv
DO  - 10.48550/arxiv.2610.06558
UR  - https://arxiv.org/abs/2610.06558
AB  - The classical Murnaghan-Nakayama rule is a recursive formula for computing the values of complex irreducible characters of the symmetric group S_n. Alun Morris proved a recursive formula for evaluating the values of irreducible spin characters of S̃_n, where S̃_n is one of the Schur covers of S_n defined by S̃_n:=⟨ t_1,t_2,⋯,t_n−1,z | z^2=1, t_i^2=z, (t_it_i+1)^3=z, t_it_j=zt_jt_i if |i−j|>1⟩. A recursive formula for evaluating the values of complex irreducible characters of the wreath product Gwr S_n, where G is a finite group, was proved by J. Stembridge. In this article, we state and prove a recursive formula to compute the values of the irreducible spin characters of the wreath product Gwr S̃_n. For the convenience of implementing these recursive formulas, we extend the notion of 0-1 boundary sequence of a Young diagram to shifted Young diagrams.
ER  -