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Berta Hudak

Publications and source records attributed to Berta Hudak.

5 recordsLinked to original sources
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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arXiv2026

On Cellularity of Hecke Algebras for Wreath Products

The (generalized) Hu algebra is a nontrivial quantization of the wreath product $\Sigma_m \wr \Sigma_d$ between symmetric groups, whose representation theory controls the Hecke algebra of the complex reflection group $G(d,d,md)$. In this paper, we construct a unified basis for this algebra and establish its cellular algebra structure in the case $d = 2$. As an application, our construction provides an elementary realization of the simple modules for the Hecke algebra of type $D_{2m}$ that are parameterized by bipartitions of size $(m,m)$.

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arXiv2024

Homomorphisms into Specht modules labelled by hooks in quantum characteristic two

Let $R_n$ denote the KLR algebra of type $A^{(1)}_{e-1}$. Using the presentation of Specht modules given by Kleschev-Mathas-Ram, Loubert completely determined $\hom_{R_n}(S^μ,S^λ)$ where $μ$ is an arbitrary partition, $λ$ is a hook and $e\neq2$. In this paper, we investigate the same problem when $e=2$. First we give a complete description of the action of the generators on the basis elements of $S^λ$. We use this result to identify a large family of partitions $μ$ such that there exists at least one non-zero homomorphism from $S^μ$ to $S^λ$, explicitly describe these maps and give their grading. Finally, we generalise James's result for the trivial module.

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