A basis and Schur-Weyl duality for the loop Hecke algebra
(2025) TBA — (2025)
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- Abstract
- The loop Hecke algebra is a generalization of the Hecke algebra to the loop braid group, introduced by Damiani, Martin and Rowell. We give a new presentation of the loop Hecke algebra provided a mild condition on the parameter and give a basis. We use higher linear rewriting theory to show linear independence and the combinatorics of Dyck paths to compute the cardinality of the basis. This yields a conjecture of Damiani-Martin-Rowel. We also give a representation theoretic interpretation of the loop Hecke algebra in terms of (non-semisimple) Schur-Weyl duality involving the negative half of quantum gl(1,1).
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Citations
Dos Santos Santana Forte Vaz, P., & et al. (2025). A basis and Schur-Weyl duality for the loop Hecke algebra. TBA. Submitted. (Original work published 2025)