The idempotents in cyclotomic Hecke algebras and periodic property of the Jucys-Murphy elements
Ge Li
TL;DR
This paper establishes a periodic property of Jucys-Murphy elements in cyclotomic Hecke algebras of type A by deriving a new, computationally efficient formula for KLR idempotents.
Contribution
It introduces a novel closed formula for KLR idempotents that simplifies computations and proves a periodicity property of Jucys-Murphy elements in these algebras.
Findings
Periodic property of Jucys-Murphy elements proven
New closed formula for KLR idempotents derived
Enhanced computational efficiency in algebraic calculations
Abstract
This paper proves a periodic property of Jucys-Murphy elements of the degenerate and non-degenerate cy- clotomic Hecke algebras of type A. We do this by first giving a new closed formula for the KLR idempotents e(i) which, it tuns out, is very efficient computationally.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Advanced Combinatorial Mathematics