An interpretation of the Lascoux-Leclerc-Thibon algorithm and graded representation theory
Alexander S. Kleshchev, David Nash
TL;DR
This paper interprets the Lascoux-Leclerc-Thibon algorithm through the lens of graded representation theory, providing a new perspective on calculating graded decomposition numbers for symmetric group algebras.
Contribution
It offers a novel interpretation of the Lascoux-Leclerc-Thibon algorithm using graded Specht modules and graded representation theory.
Findings
Calculated graded decomposition numbers for Iwahori-Hecke algebra
Revealed the Lascoux-Leclerc-Thibon algorithm as a graded representation theory process
Provided a new conceptual framework for understanding the algorithm
Abstract
We use graded Specht modules to calculate the graded decomposition numbers for the Iwahori-Hecke algebra of the symmetric group over a field of characteristic zero at a root of unity. The algorithm arrived at is the Lascoux-Leclerc-Thibon algorithm in disguise. Thus we interpret the algorithm in terms of graded representation theory.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Geometry · Advanced Topics in Algebra