Dual Murnaghan-Nakayama rule for Hecke algebras in Type $A$
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| Format: | Preprint |
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2025
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| _version_ | 1866908984980537344 |
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| author | Jing, Naihuan Liu, Ning Wu, Yu |
| author_facet | Jing, Naihuan Liu, Ning Wu, Yu |
| contents | Let $χ^λ_μ$ be the value of the irreducible character $χ^λ$ of the Hecke algebra of the symmetric group on the conjugacy class of type $μ$. The usual Murnaghan-Nakayama rule provides an iterative algorithm based on reduction of the lower partition $μ$. In this paper, we establish a dual Murnaghan-Nakayama rule for Hecke algebras of type $A$ using vertex operators by applying reduction to the upper partition $λ$. We formulate an explicit recursion of the dual Murnaghan-Nakayama rule by employing the combinatorial model of ``brick tabloids", which refines a previous result by two of us (J. Algebra 598 (2022), 24--47). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_12299 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dual Murnaghan-Nakayama rule for Hecke algebras in Type $A$ Jing, Naihuan Liu, Ning Wu, Yu Representation Theory Combinatorics Quantum Algebra Primary: 20C08, Secondary: 17B69, 05E10 Let $χ^λ_μ$ be the value of the irreducible character $χ^λ$ of the Hecke algebra of the symmetric group on the conjugacy class of type $μ$. The usual Murnaghan-Nakayama rule provides an iterative algorithm based on reduction of the lower partition $μ$. In this paper, we establish a dual Murnaghan-Nakayama rule for Hecke algebras of type $A$ using vertex operators by applying reduction to the upper partition $λ$. We formulate an explicit recursion of the dual Murnaghan-Nakayama rule by employing the combinatorial model of ``brick tabloids", which refines a previous result by two of us (J. Algebra 598 (2022), 24--47). |
| title | Dual Murnaghan-Nakayama rule for Hecke algebras in Type $A$ |
| topic | Representation Theory Combinatorics Quantum Algebra Primary: 20C08, Secondary: 17B69, 05E10 |
| url | https://arxiv.org/abs/2503.12299 |