Martín Forsberg Conde

arXiv2026

Homomorphisms to Hook Specht Modules over Quiver Hecke Algebras of Type C

We investigate homomorphisms between Specht modules for level 1 cyclotomic quiver Hecke algebras of affine type C. For hook partitions with a `short leg' or a `short arm', we give the full quiver Hecke algebra action and we show that every non-zero homomorphism from an arbitrary Specht module is determined by sending the cyclic generator to a single standard basis element. We use this action to investigate homomorphisms to these Specht modules, giving a full classification in the short leg case. This provides the first investigation of homomorphisms between Specht modules in affine type C and extends methods previously used in affine type A.

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arXiv2025

A generalization of Carter-Payne homomorphisms

We construct graded homomorphisms between Specht modules of quiver Hecke algebras of type A that differ by an ``$e$-small'' partition-shaped removable set of nodes by expanding on methods by Lyle and Mathas. Our main result constitutes a full generalization of the classical result by Carter and Payne for Specht modules of the symmetric group.

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