RSK superinsertion and super Frobenius formulae
Deke Zhao
TL;DR
This paper extends the RSK superinsertion algorithm to hook-multipartitions and derives a super Frobenius formula for cyclotomic Hecke algebra characters, providing new proofs and insights into their structure.
Contribution
It introduces a generalized RSK superinsertion algorithm for hook-multipartitions and derives the super Frobenius formula for cyclotomic Hecke algebra characters, including a new proof of Mitsuhashi's formula.
Findings
Extended RSK superinsertion to hook-multipartitions.
Derived super Frobenius formula for cyclotomic Hecke algebra characters.
Provided a new proof of Mitsuhashi's super Frobenius formula.
Abstract
In this paper we extend the Robinson-Schensted-Knuth (RSK) superinsertion algorithm to hook-multipartitions and derive the super Frobenius formula for the characters of cyclotomic Hecke algebras (Linear and Multilinear Algebra, DOI: 10.1080/03081087.2019.1663140) via the RSK superinsertion algorithm. In particular, we obtain a new proof of Mitsuhashi's super Frobenius formula for the characters of Iwahori-Hecke algebras.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Advanced Algebra and Geometry