Graded induction for Specht modules
Jun Hu, Andrew Mathas
TL;DR
This paper proves a conjecture by demonstrating that induced Specht modules in cyclotomic Hecke algebras have an explicit filtration by graded Specht modules, advancing understanding of their graded structure.
Contribution
It establishes an explicit filtration of induced Specht modules by graded Specht modules, confirming a conjecture in the field.
Findings
Induced Specht modules have an explicit filtration by shifts of graded Specht modules.
The result confirms a conjecture of Brundan, Kleshchev, and Wang.
Advances the understanding of graded structures in cyclotomic Hecke algebras.
Abstract
Recently Brundan, Kleshchev and Wang introduced a -grading on the Specht modules of the degenerate and non-degenerate cyclotomic Hecke algebras of type . In this paper we show that induced Specht modules have an explicit filtration by shifts of graded Specht modules. This proves a conjecture of Brundan, Kleshchev and Wang.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Geometry · Advanced Topics in Algebra