Séminaire Lotharingien de Combinatoire, 93B.96 (2025), 12 pp.
Robert Muth, Thomas Nicewicz, Liron Speyer and Louise Sutton
Simple Modules for Affine Type A KLR/I> Algebras via Skew Specht Modules
Abstract.
Cuspidal systems parameterise KLR algebra representations via root partitions π, where simple modules L(π) arise as heads of proper standard modules.
We define a combinatorial dilation map and construct skew Young diagrams ζ(π) associated to each root partition π in an arbitrary convex order in affine type A.
These skew diagrams have the property that the corresponding skew Specht module
Sζ(π) has simple head L(π) and a filtration by proper standard modules.
Our results represent a far more explicit and combinatorial construction of these modules than was previously known.
Received: November 15, 2024.
Accepted: February 15, 2025.
Final version: April 1, 2025.
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