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4 papers · 2 filters
An interpretation of the Lascoux-Leclerc-Thibon algorithm and graded representation theory
Alexander S. Kleshchev, David Nash
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 uni…
Representation Theory of Symmetric Groups and Related Hecke Algebras
Alexander Kleshchev
This is an expository article. We survey some fundamental trends in representation theory of symmetric groups and related objects which became apparent in the last fifteen years. T…
Representations of Khovanov-Lauda-Rouquier Algebras and Combinatorics of Lyndon Words
Alexander Kleshchev, Arun Ram
We construct irreducible representations of affine Khovanov-Lauda-Rouquier algebras of arbitrary finite type. The irreducible representations arise as simple heads of appropriate i…
Graded decomposition numbers for cyclotomic Hecke algebras
Jonathan Brundan, Alexander Kleshchev
In recent joint work with Wang, we have constructed graded Specht modules for cyclotomic Hecke algebras. In this article, we prove a graded version of the Lascoux-Leclerc-Thibon co…